arXiv:1912.02553by: Orlando, DomenicoAbstract: Integrable deformations of type IIB superstring theory on $\mathrm{AdS}_5\times S^5$ have played an important role over the last years. The Yang-Baxter deformation is a systematic way of generating such integrable deformations. Since its introduction, this topic has seen important conceptual progress and has among others led to the intriguing discovery generalized supergravity, a new low-energy effective theory. This review endeavors to not only introduce the historical development of the Yang-Baxter deformation, but also its relation to generalized supergravity, non-geometric backgrounds, non-abelian T-duality and preserved Killing spinors. We supplement the general treatment with a wealth of explicit examples. […]

arXiv:1911.06008by: Aneesh, P.B. (Chennai Math. Inst.) et al.Abstract: In [1], two of the present authors along with P. Raman attempted to extend the Amplituhedron program for scalar field theories [2] to quartic scalar interactions. In this paper we develop various aspects of this proposal. Using recent seminal results in Representation theory [3,4], we show that projectivity of scattering forms and existence of kinematic space associahedron completely capture planar amplitudes of quartic interaction. We generalise the results of [1] and show that for any $n$-particle amplitude, the positive geometry associated to the projective scattering form is a convex realisation of Stokes polytope which can be naturally embedded inside one of the ABHY associahedra defined in [2,5]. For a special class of Stokes polytopes with hyper-cubic topology, we show that they have a canonical convex realisation in kinematic space as boundaries of kinematic space associahedra. We then use these kinematic space geometric constructions to write worldsheet forms for $\phi^{4}$ theory which are forms of lower rank on the CHY moduli space. We argue that just as in the case of bi-adjoint $\phi^3$ scalar amplitudes, scattering equations can be used as diffeomorphisms between certain $\frac{n-4}{2}$ forms on the worldsheet and $\frac{n-4}{2}$ forms on ABHY associahedron that generate quartic amplitudes. […]

arXiv:1910.11273by: Aschieri, Paolo (Piemonte Orientale U., Alessandria) et al.Abstract: We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly restrict to Dirac structures. Depending on an auxiliary affine connection K, we introduce the K-curvature and K-torsion of a Courant algebroid connection. These are conventional tensors on the body. Finally, we compute their Ricci and scalar curvature. […]

arXiv:1910.06332by: Bianchi, Lorenzo (Queen Mary, U. of London) et al.Abstract: In conformal $\mathcal{N}=2$ Super Yang-Mills theory, the energy emitted by an accelerated heavy particle is computed by the one-point function of the stress tensor operator in the presence of a Wilson line. In this paper, we consider the theory on the ellipsoid and we prove a conjectured relation between the stress tensor one-point function and the first order expansion of the Wilson loop expectation value in the squashing parameter. To do this, we analyze the behavior of the Wilson loop for a small deformation of the background geometry and, at first order in the deformation, we fix the kinematics using defect CFT constraints. In the final part of the paper, we analyze the consequences of our results for the weak coupling perturbative expansion. In particular, comparing the weakly coupled matrix model with the ordinary Feynman diagram expansion, we find a natural transcendentality driven organization for the latter. […]

arXiv:1910.03508by: Andrianopoli, L. (Turin Polytechnic) et al.Abstract: We derive a $2+1$ dimensional model with unconventional supersymmetry at the boundary of an ${\rm AdS}_4$ $\mathcal{N}$-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene at the two Dirac points, ${\bf K}$ and ${\bf K}'$. The two valleys correspond to the two independent sectors of the ${\rm OSp}(p|2)\times {\rm OSp}(q|2)$ boundary model in the $p=q$ case, which are related by a parity transformation. The Semenoff and Haldane-type masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model. […]

arXiv:1910.03347by: Angelantonj, Carlo (INFN, Turin) et al.Abstract: It is shown that the generating function of $\mathscr{N}=2$ topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background. This background, which corresponds to an exact CFT, realises in string theory the six-dimensional $\varOmega$-background of Nekrasov, in the case of opposite deformation parameters $\epsilon_1=-\epsilon_2$, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. The analysis is performed on both heterotic and type I strings and for the cases of ordinary $\mathscr{N}=2$ and $\mathscr{N}=2^*$ theories. […]

arXiv:1909.11675by: Erler, Theodore (ASCR, Prague) et al.Abstract: Generalizing previous work, we give a new analytic solution in Witten's open bosonic string field theory which can describe any open string background. The central idea is to use Riemann surface degenerations as a mechanism for taming OPE singularities. This requires leaving the familiar subalgebra of wedge states with insertions, but the payoff is that the solution makes no assumptions about the reference and target D-brane systems, and is therefore truly general. For example, unlike in previous work, the solution can describe time dependent backgrounds and multiple copies of the reference D-brane within the universal sector. The construction also resolves some subtle issues resulting from associativity anomalies, giving a more complete understanding of the relation between the degrees of freedom of different D-brane systems, and a nonperturbative proof of background independence in classical open bosonic string field theory. […]

arXiv:1909.08642CP3-Origins-2019-36 DNRF90by: Orlando, Domenico (INFN, Turin) et al.Abstract: We investigate four-dimensional near-conformal dynamics by means of the large-charge limit. We first introduce and justify the formalism in which near-conformal invariance is insured by adding a dilaton and then determine the large-charge spectrum of the theory. The dilaton can also be viewed as the radial mode of the EFT. We calculate the two-point functions of charged operators. We discover that the mass of the dilaton, parametrising the near-breaking of conformal invariance, induces a novel term that is logarithmic in the charge. One can therefore employ the large-charge limit to explore near-conformal dynamics and determine dilaton-related properties. […]

arXiv:1909.02571by: Alvarez-Gaume, Luis (Stony Brook U., New York, SCGP) et al.Abstract: We apply the large-charge expansion to O(N) vector models starting from first principles, focusing on the Wilson-Fisher point in three dimensions. We compute conformal dimensions at zero and finite temperature at fixed charge Q, concentrating on the regime $1 \ll N \ll Q$. Our approach places the earlier effective field theory treatment on firm ground and extends its predictions. […]

arXiv:1908.00029by: Gliozzi, Ferdinando (INFN, Turin)Abstract: The modular bootstrap program for 2d CFTs could be seen as a systematic exploration of the physical consequences of consistency conditions at the elliptic points and at the cusp of their toruspartition function. The study at $\tau=i$, the elliptic point stabilized by the modular inversion $S$, was initiated by Hellerman, who found a general upper bound for the most relevant scaling dimension $\Delta$. Likewise, analyticity at $\tau=i\infty$, the cusp stabilized by the modular translation $T$, yields an upper bound on the twist gap. Here we study consistency conditions at $\tau=\exp[2i\pi/3]$, the elliptic point stabilized by $S T$. We find a much stronger upper bound in the large-c limit, namely $\Delta […]

arXiv:1907.07152ARC-19-08by: Cremonini, C.A. (Milan U.) et al.Abstract: We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudo-forms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators. We provide several examples of computation of PCO's acting on different type of forms. We illustrate also the action of the $\eta$ operator, crucial ingredient to define the interactions of super Chern-Simons theory. Then, we discuss the action for super Chern-Simons theory on any supermanifold, first in the factorized form (3-form $\times$ PCO) and then, we consider the most general expression. The latter is written in term of psuedo-forms containing an infinite number of components. We show that the free equations of motion reduce to the usual Chern-Simons equations yielding the proof of the equivalence between the formulations at different pictures of the same theory. Finally, we discuss the interaction terms. They require a suitable definition in order to take into account the picture number. That implies the construction of a 2-product which is not associative that inherits an $A_\infty$ algebra structure. That shares several similarities with a recent construction of a super string field theory action by Erler, Konopka and Sachs. […]

arXiv:1907.03759KUNS-2767by: Orlando, Domenico (Turin U.) et al.Abstract: In this note, we study the action of $O(d,d)$ transformations on the integrable structure of two-dimensional non-linear sigma models via the doubled formalism. We construct the Lax pairs associated with the $O(d,d)$-transformed model and find that they are in general non-local because they depend on the winding modes. We conclude that every $O(d,d;\mathbb{R})$ deformation preserves integrability. As an application we compute the Lax pairs for continuous families of deformations, such as $J\bar{J}$ marginal deformations and TsT transformations of the three-sphere with $H$-flux. […]

arXiv:1906.11672ARC-19-07by: Fré, P. (Turin U.) et al.Abstract: Considering matter coupled supersymmetric Chern-Simons theories in three dimensions we extend the Gaiotto-Witten mechanism of supersymmetry enhancement $\mathcal{N}_3=3\to \mathcal{N}_3=4$ from the case where the hypermultiplets span a flat HyperK\"ahler manifold to that where they live on a curved one. We derive the precise conditions of this enhancement in terms of generalized Gaiotto-Witten identities to be satisfied by the tri-holomorphic moment maps. An infinite class of HyperK\"ahler metrics compatible with the enhancement condition is provided by the Calabi metrics on $T^\star \mathbb{P}^{n}$. In this list we find, for $n=2$ the resolution of the metric cone on $\mathrm{N}^{0,1,0}$ which is the unique homogeneous Sasaki Einstein 7-manifold leading to an $\mathcal{N}_4=3$ compactification of M-theory. This leads to challenging perspectives for the discovery of new relations between the enhancement mechanism in $D=3$, the geometry of M2-brane solutions and also for the dual description of super Chern Simons theories on curved HyperK\"ahler manifolds in terms of gauged fixed supergroup Chern Simons theories. The relevant supergroup is in this case $\mathrm{SU(3|N)}$ where $\mathrm{SU(3)}$ is the flavor group and $\mathrm{U(N)}$ is the color group. […]

arXiv:1906.07085JHEP 1908 (2019) 108by: Billò, M. (Turin U.) et al.Abstract: We consider the 1/2 BPS circular Wilson loop in a generic $ \mathcal{N} $ = 2 SU(N) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite N and in the large-N limit, using the interacting matrix model provided by localization results. We single out some families of theories for which the Wilson loop vacuum expectation values approaches the $ \mathcal{N} $ = 4 result in the large-N limit, in agreement with the fact that they possess a simple holographic dual. At finite N and in the generic case, we explicitly compare the matrix model result with the field-theory perturbative expansion up to order g$^{8}$ for the terms proportional to the Riemann value ζ (5), finding perfect agreement. Organizing the Feynman diagrams as suggested by the structure of the matrix model turns out to be very convenient for this computation. […]

arXiv:1905.10898JHEP 1907 (2019) 177by: Ballav, Sourav (HBNI, Mumbai) et al.Abstract: We study half-BPS surface operators in $ \mathcal{N} $ = 2 supersymmetric QCD in four dimensions with gauge group SU(2) and four fundamental flavours. We compute the twisted chiral superpotential that describes the effective theory on the surface operator using equivariant localization as well as the Seiberg-Witten data. We then use the constraints imposed by S-duality to resum the instanton contributions to the twisted superpotential into elliptic functions and (quasi-) modular forms. The resummed results match what one would obtain from the description of surface operators as the insertion of a degenerate operator in a spherical conformal block in Liouville CFT. […]

arXiv:1905.04958JHEP 1906 (2019) 101by: Maccaferri, Carlo (Turin U.) et al.Abstract: We consider the algebraic effective couplings for open superstring massless modes in the framework of the $A_\infty$ theory in the small Hilbert space. Focusing on quartic algebraic couplings, we reduce the effective action of the $A_\infty$ theory to the Berkovits one where we have already shown that such couplings are fully computed from contributions at the boundary of moduli space, when the massless fields under consideration are appropriately charged under an ${\cal N}\!=\!2$ $R$-symmetry. Here we offer a proof of localization which is in the small Hilbert space. We also discuss the flat directions of the obtained quartic potentials and give evidence for the existence of exactly marginal deformations in the $D3/D(-1)$ system in the framework of string field theory. […]

arXiv:1905.00026JHEP 1908 (2019) 164by: Orlando, Domenico (INFN, Turin) et al.Abstract: We apply the large-charge limit to the first known example of a four-dimensional gauge-Yukawa theory featuring an ultraviolet interacting fixed point in all couplings. We determine the energy of the ground state in presence of large fixed global charges and deduce the global symmetry breaking pattern. We show that the fermions decouple at low energy leaving behind a confining Yang-Mills theory and a characteristic spectrum of type I (relativistic) and type II (non-relativistic) Goldstone bosons. Armed with the knowledge acquired above we finally arrive at establishing the conformal dimensions of the theory as a triple expansion in the large-charge, the number of flavors and the controllably small inverse gauge coupling constant at the UV fixed point. Our results unveil a number of noteworthy properties of the low-energy spectrum, vacuum energy and conformal properties of the theory. They also allow us to derive a new consistency condition for the relative sizes of the couplings at the fixed point. […]

arXiv:1903.04431ARC-18-18JHEP 1906 (2019) 036by: Andrianopoli, L. (Turin Polytechnic) et al.Abstract: We consider AdS$_{3}$N-extended Chern-Simons supergravity (à la Achucarro-Townsend) and we study its gauge symmetries. We promote those gauge symmetries to a BRST symmetry and we perform its quantization by choosing suitable gauge-fixings. The resulting quantum theories have different features which we discuss in the present work. In particular, we show that a special choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez, Valenzuela and Zanelli for the graphene fermion. […]

arXiv:1902.09542Phys.Rev.Lett. 123 (2019) 051603by: Banerjee, Debasish (Humboldt U., Berlin) et al.Abstract: We study the O(4) Wilson-Fisher fixed point in 2+1 dimensions in fixed large-charge sectors identified by products of two spin-j representations (jL,jR). Using effective field theory we derive a formula for the conformal dimensions D(jL,jR) of the leading operator in terms of two constants, c3/2 and c1/2, when the sum jL+jR is much larger than the difference |jL-jR|. We compute D(jL,jR) when jL=jR with Monte Carlo calculations in a discrete formulation of the O(4) lattice field theory, and show excellent agreement with the predicted formula and estimate c3/2=1.068(4) and c1/2=0.083(3). […]

arXiv:1902.01060J.Geom.Phys. 145 (2019) 103467by: Bruzzo, Ugo (INFN, Trieste) et al.Abstract: As a continuation of a general program started in two previous publications, in the present paper we study the K\"ahler quotient resolution of the orbifold $\mathbb{C}^3/\mathbb{Z}_4$, comparing with the results of a toric description of the same. In this way we determine the algebraic structure of the exceptional divisor, whose compact component is the second Hirzebruch surface $\mathbb F_2$. We determine the explicit K\"ahler geometry of the smooth resolved manifold $Y$, which is the total space of the canonical bundle of $\mathbb F_2$. We study in detail the chamber structure of the space of stability parameters (corresponding in gauge theory to the Fayet-Iliopoulos parameters) that are involved in the construction of the desingularizations either by generalized Kronheimer quotient, or as algebro-geometric quotients. The walls of the chambers correspond to two degenerations; one is a partial desingularization of the quotient, which is the total space of the canonical bundle of the weighted projective space $\mathbb P[1,1,2]$, while the other is the product of the ALE space $A_1$ by a line, and is related to the full resolution in a subtler way. These geometrical results will be used to look for exact supergravity brane solutions and dual superconformal gauge theories. […]

arXiv:1901.09693ROM2F/2019/02JHEP 1905 (2019) 199by: Billo, M. (Turin U.) et al.Abstract: We study the two-point correlation functions of chiral/anti-chiral operators in $ \mathcal{N} $ = 2 supersymmetric Yang-Mills theories on $ \mathbb{R}^{4}$ with gauge group SU(N) and N$_{f}$ massless hypermultiplets in the fundamental representation. We compute them in perturbation theory, using dimensional regularization up to two loops, and show that field-theory observables built out of dimensionless ratios of two-point renormalized correlators on $ \mathbb{R}^{4}$ are in perfect agreement with the same quantities computed using localization on the four-sphere, even in the non-conformal case N$_{f}$ ≠ 2N. […]

arXiv:1901.09630Eur.Phys.J. C79 (2019) 372by: Ashok, Sujay K. (HBNI, Mumbai) et al.Abstract: We study half-BPS surface operators in $\mathcal {N}=2$ supersymmetric asymptotically conformal gauge theories in four dimensions with SU(N) gauge group and 2N fundamental flavours using localization methods and coupled 2d/4d quiver gauge theories. We show that contours specified by a particular Jeffrey–Kirwan residue prescription in the localization analysis map to particular realizations of the surface operator as flavour defects. Seiberg duality of the 2d/4d quivers is mapped to contour deformations of the localization integral which in this case involves a residue at infinity. This is reflected as a modified Seiberg duality rule that shifts the Lagrangian of the purported dual theory by non-perturbative terms. The new rules, that depend on the 4d gauge coupling, lead to a match between the low energy effective twisted chiral superpotentials for any pair of dual 2d/4d quivers. […]

arXiv:1901.08038JHEP 1906 (2019) 027by: Erler, Theodore (Prague, Inst. Phys.) et al.Abstract: Motivated by the appearance of associativity anomalies in the context of superstring field theory, we give a generalized solution built from boundary condition changing operators which can be associated to a generic tachyon vacuum in the KBc subalgebra of the Okawa form. We articulate sufficient conditions on the choice of tachyon vacuum to ensure that ambiguous products do not appear in the equations of motion. […]

arXiv:1901.00818ARC-18-14Annales Henri Poincare 20 (2019) 4163-4195by: Catenacci, Roberto (Piemonte Orientale U., Alessandria) et al.Abstract: Inspired by the analogy between different types of differential forms on supermanifolds and string fields in superstring theory, we construct new multilinear non-associative products of forms which yield an $A_\infty$-algebra. […]

arXiv:1812.06915ARC-18-20Phys.Lett. B789 (2019) 496-501by: Angelantonj, Carlo (Turin U.) et al.Abstract: We present a class of heterotic compactifications where it is possible to lower the string unification scale down to the GUT scale, while preserving the validity of the perturbative analysis. We illustrate this approach with an explicit example of a four-dimensional chiral heterotic vacuum with N=1 supersymmetry. […]

arXiv:1812.04643Nucl.Phys. B941 (2019) 158-194by: Finotello, Riccardo (INFN, Turin) et al.Abstract: We consider the classical instantonic contribution to the open string configuration associated with three D-branes with relative rotation matrices in SO(4) which corresponds to the computation of the classical part of the correlator of three non Abelian twist fields. We write the classical solution as a sum of a product of two hypergeometric functions. Differently from all the previous cases with three D-branes, the solution is not holomorphic and suggests that the classical bosonic string knows when the configuration may be supersymmetric. We show how this configuration reduces to the standard Abelian twist field computation. From the phenomenological point of view, the Yukawa couplings between chiral matter at the intersection in this configuration are more suppressed with respect to the factorized case in the literature. […]

arXiv:1811.11764Phys.Scripta 94 (2019) 095001by: Orlando, Domenico (Turin U.) et al.Abstract: In this note we give an explicit formula for the preserved Killing spinors in deformed string theory backgrounds corresponding to integrable Yang–Baxter deformations realized via (sequences of) TsT transformations. The Killing spinors can be expressed only in terms of the bi-vector Θ which encodes the deformation. This formula is applicable to deformed backgrounds related to r-matrices of various ranks, including those that do not satisfy the unimodularity condition and give rise to backgrounds in generalized supergravity. We conjecture that our formula also remains valid for integrable deformations which are not realized via TsT transformations and motivate this conjecture by explicit examples. […]

arXiv:1810.03624ARC-18-06by: Castellani, LeonardoAbstract: It is convenient to describe a quantum system at all times by means of a "history operator" $C$, encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of measurement sequences, and generalize the "sum over position histories " of the Feynman path-integral. As we argue in the present note, this description has some computational advantages over the usual state vector description, and may help to clarify some issues regarding nonlocality of quantum correlations and collapse. A measurement on a system described by $C$ modifies the history operator, $C \rightarrow PC$, where $P$ is the projector corresponding to the measurement. We refer to this modification as "history operator collapse". Thus $C$ keeps track of the succession of measurements on a system, and contains all histories compatible with the results of these measurements. The collapse modifies the history content of $C$, and therefore modifies also the past (relative to the measurement), but never in a way to violate causality. Probabilities of outcomes are obtained as $Tr(C^\dagger P C)/Tr(C^\dagger C)$. A similar formula yields probabilities for intermediate measurements, and reproduces the result of the two-vector formalism in the case of given initial and final states. We apply the history operator formalism to a few examples: entangler circuit, Mach-Zehnder interferometer, teleportation circuit, three-box experiment. Not surprisingly, the propagation of coordinate eigenstates $|q\rangle$ is described by a history operator $C$ containing the Feynman path-integral. […]

arXiv:1809.06371JHEP 1812 (2018) 052by: Favrod, Samuel (Zurich, ETH) et al.Abstract: In this note, we perform the large-charge expansion for non-relativistic systems with a global U(1) symmetry in 3 + 1 and 2 + 1 space-time dimensions, motivated by applications to the unitary Fermi gas and anyons. These systems do not have full conformal invariance, but are invariant under the Schrödinger group. Also here, the low-energy physics is encoded by a Goldstone boson which is due to the breaking of the global symmetry when fixing the charge. We find that in 2 + 1 dimensions and higher, there is a large-charge expansion in which quantum corrections are suppressed with respect to the next-to-leading order terms in the Lagrangian. We give the next-to-leading-order expressions for the ground state energy and the speed of sound. […]

arXiv:1809.05426Annales Henri Poincare 20 (2019) 3197-3227by: Aschieri, Paolo (Piemonte Orientale U., Alessandria) et al.Abstract: Seiberg–Witten maps are a well-established method to locally construct noncommutative gauge theories starting from commutative gauge theories. We revisit and classify the ambiguities and the freedom in the definition. Geometrically, Seiberg–Witten maps provide a quantization of bundles with connections. We study the case of U(n)-vector bundles on two-dimensional tori, prove the existence of globally defined Seiberg–Witten maps (induced from the plane to the torus) and show their compatibility with Morita equivalence. […]

arXiv:1807.09563DISIT-18ARC-18-05J.Geom.Phys. 148 (2020) 103559by: Catenacci, R. (Piemonte Orientale U., Alessandria) et al.Abstract: Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaf-theoretical point of view. In particular, the formal distributional properties of integral forms are recovered in this scenario in a geometrical way. Further, we show how inverse forms extend the ordinary de Rham complex on a supermanifold, thus providing a mathematical foundation of the Large Hilbert Space used in superstrings. Last, we briefly discuss how the Hodge diamond of a supermanifold looks like, and we explicitly compute it for super Riemann surfaces. […]

arXiv:1807.06316Eur.Phys.J. C79 (2019) 278by: Ashok, S.K. (IMSc, Chennai) et al.Abstract: We study half-BPS surface operators in four dimensional ${{{\mathcal {N}}}}=2$ SU(N) gauge theories, and analyze their low-energy effective action on the four dimensional Coulomb branch using equivariant localization. We also study surface operators as coupled 2d/4d quiver gauge theories with an SU(N) flavour symmetry. In this description, the same surface operator can be described by different quivers that are related to each other by two dimensional Seiberg duality. We argue that these dual quivers correspond, on the localization side, to distinct integration contours that can be determined by the Fayet-Iliopoulos parameters of the two dimensional gauge nodes. We verify the proposal by mapping the solutions of the twisted chiral ring equations of the 2d/4d quivers onto individual residues of the localization integrand. […]

arXiv:1806.01841by: Aschieri, PaoloAbstract: We study noncommutative principal bundles (Hopf--Galois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasi-commutative, and thus the base space subalgebra is central, we define the gauge group as the group of vertical automorphisms or equivalently as the group of equivariant algebra maps. We study Drinfeld twist (2-cocycle) deformations of Hopf--Galois extensions and show that the gauge group of the twisted extension is isomorphic to the gauge group of the initial extension. In particular noncommutative principal bundles arising via twist deformation of commutative principal bundles have classical gauge group. We illustrate the theory with a few examples. […]

arXiv:1805.00948KUNS-2731J.Phys. A51 (2018) 395401by: Orlando, Domenico (INFN, Turin) et al.Abstract: The Yang–Baxter deformation (yb deformation) is a systematic way of performing integrable deformations of 2D symmetric non-linear sigma models. The deformations can be labeled by classical r-matrices satisfying the classical yb equation. This yb deformation is also applicable to type IIB superstring theory defined on AdS. In this case, a simple class of yb deformations is associated with TsT transformations of string backgrounds. The data of this transformation is encoded in an antisymmetric bi-vector Θ (which is often called β field or non-commutativity parameter). In this article, we give a simple recipe for obtaining the explicit expression for the Killing spinors of the TsT transformed background starting from Θ. We moreover discuss the M-theory equivalent of the TsT transformation, allowing us to also give Killing spinors of 11D backgrounds. We discuss examples of TsT transformed backgrounds starting from flat space, and . We find that in this way we can relate the Ω-deformation to yb deformations. […]

arXiv:1804.04151Nucl.Phys. B934 (2018) 437-458by: Loukas, Orestis (U. Bern, AEC) et al.Abstract: Considering theories in sectors of large global charge Q results in a semiclassical effective field theory ( eft ) description for some strongly-coupled conformal field theories ( cfts ) with continuous global symmetries. Hence, when studying dualities at large charge, we can have control over the strongly coupled side of the duality and gain perturbative access to both dual pairs. […]

arXiv:1804.01535CALT-TH-2018-014IPMU18-0059by: Hellerman, Simeon (Tokyo U., IPMU) et al.Abstract: Carrying to higher precision the large-$\mathcal{J}$ expansion of Hellerman and Maeda, we calculate to all orders in $1/\mathcal{J}$ the power-law corrections to the two-point functions $\mathcal{Y}_n \equiv |x - y|^{2n\Delta_{\mathcal{O}}} \langle {\mathcal{O}}_n(x) \bar{\mathcal{O}}_n(y) \rangle$ for generators $\mathcal{O}$ of Coulomb branch chiral rings in four-dimensional $\mathcal{N} =2$ superconformal field theories. We show these correlators have the universal large-$n$ expansion \[ \log(\mathcal{Y}_n) \simeq \mathcal{J} \mathbf{A} + \mathbf{B} + \log(\Gamma( \mathcal{J} + \alpha + 1)) , \] where $\mathcal{J} \equiv 2 n \Delta_{\mathcal{O}}$ is the total $R$-charge of $\mathcal{O}_n$, the $\mathbf{A}$ and $\mathbf{B}$ are theory-dependent coefficients, $\alpha$ is the coefficient of the Wess-Zumino term for the Weyl $a$-anomaly, and the $\simeq$ denotes equality up to terms exponentially small in $\mathcal{J}$. Our methods combine the structure of the Coulomb-branch effective field theory (EFT) with the supersymmetric recursion relations. However, our results constrain the power-law corrections to all orders, even for non-Lagrangian theories to which the recursion relations do not apply. For the case of $\mathcal{N} = 2$ SQCD, we also comment on the nature of the exponentially small corrections, which can be calculated to high precision in the double-scaling limit recently discussed by Bourget et al. We show the exponentially small correction is consistent with the interpretation of the EFT breaking down due to the propagation of massive BPS particles over distances of order of the infrared scale $|x - y|$. […]

PoS EPS-HEP2017 (2017) 546by: Samsonyan, Marine (CERN) et al.Abstract: We present a D-brane realisation of the Abelian and non-Abelian N = 2 ∗ theory both in five and four dimensions. We compute topological amplitudes in string theory for Ω deformed spacetime first with one and then with two parameters. In the field theory limit we recover the perturbative partition function of the deformed N = 2 ∗ theory in agreement with the existing literature. […]

arXiv:1803.05916JHEP 1806 (2018) 136by: Lambert, Neil (King's Coll. London, Dept. Math) et al.Abstract: We consider supersymmetric deformations of gauge theories in various dimensions obtained from a String Theory realisation of branes embedded in flux backgrounds. In particular we obtain deformations which take the form of Wilson line defects, also obtained by a twisting of the R-symmetry into the gauge symmetry. Furthermore we construct higher-order generalisations, also expressed a twisting of the R-symmetry, that have symmetries associated to co-dimension two and three defects. […]

ARC-18-03arXiv:1802.09813JHEP 1803 (2018) 193by: Billo, M. (Turin U.) et al.Abstract: We consider conformal N=2 super Yang-Mills theories with gauge group SU(N) and Nf=2N fundamental hypermultiplets in presence of a circular 1/2-BPS Wilson loop. It is natural to conjecture that the matrix model which describes the expectation value of this system also encodes the one-point functions of chiral scalar operators in presence of the Wilson loop. We obtain evidence of this conjecture by successfully comparing, at finite N and at the two-loop order, the one-point functions computed in field theory with the vacuum expectation values of the corresponding normal-ordered operators in the matrix model. For the part of these expressions with transcendentality zeta(3), we also obtain results in the large-N limit that are exact in the 't Hooft coupling lambda. […]

arXiv:1802.03407ARC-18-02Fortsch.Phys. 66 (2018) 1800014by: Castellani, Leonardo (Piemonte Orientale U., Alessandria)Abstract: We review the group‐geometric approach to supergravity theories, in the perspective of recent developments and applications. Usual diffeomorphisms, gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a supergroup manifold. Integration on supermanifolds is briefly revisited, and used as a tool to provide a bridge between component and superspace actions. As an illustration of the constructive techniques, the cases of off‐shell supergravities and Chern‐Simons supergravity are discussed in detail. A cursory account of supergravity is also included. We recall a covariant canonical formalism, well adapted to theories described by Lagrangians d‐forms, that allows to define a form hamiltonian and to recast constrained hamiltonian systems in a covariant form language. Finally, group geometry and properties of spinors and gamma matrices in dimensions are summarized in Appendices. […]

arXiv:1801.08081JHEP 1804 (2018) 007by: Andrianopoli, L. (Turin Polytechnic) et al.Abstract: In this paper we perform, in the spirit of the holographic correspondence, a particular asymptotic limit of N=2, AdS_4 supergravity to N=2 supergravity on a locally AdS_3 boundary. Our boundary theory enjoys OSp(2|2) x SO(1,2) invariance and is shown to contain the D=3 super-Chern Simons OSp(2|2) theory considered in [Alvarez:2011gd] and featuring "unconventional local supersymmetry". The model constructed in that reference describes the dynamics of a spin-1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to be relevant for the description of graphene, near the Dirac points, for specific spatial geometries. Our construction yields the model in [Alvarez:2011gd] with a specific prescription on the parameters. In this framework the Dirac spin-1/2 fermion originates from the radial components of the gravitini in D=4. […]

arXiv:1801.07607JHEP 1803 (2018) 112by: Maccaferri, Carlo (INFN, Turin) et al.Abstract: We consider the construction of the algebraic part of D-branes tree-level effective action from Berkovits open superstring field theory. Applying this construction to the quartic potential of massless fields carrying a specific worldsheet charge, we show that the full contribution to the potential localizes at the boundary of moduli space, reducing to elementary two-point functions. As examples of this general mechanism, we show how the Yang-Mills quartic potential and the instanton effective action of a Dp/D(p − 4) system are reproduced. […]

ARC-18-01arXiv:1801.04854Universe 4 (2018) 60by: Catenacci, Roberto (Rome U.) et al.Abstract: We use the techniques of integral forms to analyse the easiest example of two dimensional sigma models on a supermanifold. We write the action as an integral of a top integral form over a D=2 supermanifold and we show how to interpolate between different superspace actions. Then, we consider curved supermanifolds and we show that the definitions used for flat supermanifold can also be used for curved supermanifolds. We prove it by first considering the case of a curved rigid supermanifold and then the case of a generic curved supermanifold described by a single superfield $E$. […]

arXiv:1712.06946ARC-17-12JHEP 1805 (2018) 046by: Ashok, S.K. (IMSc, Chennai) et al.Abstract: We study half-BPS surface operators in 5d $ \mathcal{N} $ = 1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations, we obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities. […]

by: Rajan John, Renjan (Chennai Math. Inst.)Abstract: In this thesis, we study gauge theories with N = 2 supersymmetry in four dimensions. The low energy effective action of these theories on their Coulomb branch is described by a holomorphic function called the prepotential. In the first half, we study linear conformal quiver theories with gauge group SU(2). These theories have an SU(2) gauge group at each node of the quiver, and matter arranged in the fundamental and the bi-fundamental representations, such that at each node the beta-function vanishes. To compute the prepotential for these theories, we follow three different approaches. These are (i) the classic Seiberg-Witten approach, in which we consider an M-theory construction of the Seiberg-Witten curve and the associated differential, (ii) equivariant localization as developed by Nekrasov, and (iii) the 2d/4d correspondence of the four dimensional gauge theory with the two dimensional Liouville conformal field theory, as put forward by Alday, Gaiotto, and Tachikawa. Matching the prepotential, we find out the precise map between the various parameters that appear in the three descriptions. In the latter half of the thesis, we study surface operators in the context of N=2* theories with gauge group SU(N). These theories describe the dynamics of a vector multiplet, and a massive hypermultiplet in the adjoint representation of the gauge group. Surface operators are non-local operators that have support on a two dimensional sub-manifold of the four dimensional spacetime. They are defined by the singularities they induce in the four-dimensional gauge fields, or can be characterized by the two-dimensional theory they support on their world-volume. The infrared dynamics on the world-volume of the two-dimensional surface operator is described by a holomorphic function called the twisted superpotential. Using localization techniques, we obtain the instanton partition function, and thereby the twisted superpotential of these theories. This involves taking a suitable orbifold of the original action without the surface operator. Imposing constraints from S-duality, we obtain a modular anomaly equation for the coefficients that appear in the mass expansion of the twisted superpotential. Solving the modular anomaly equation at each order, and comparing with the results obtained from localization, we resum the twisted superpotential in a mass series, whose coefficient functions depend on (quasi-) modular forms and elliptic functions of the bare coupling constant and the continuous (complex) parameters that describe the surface operator. We further show that our results for monodromy defects in the four-dimensional theory, match the effective twisted superpotential that describes the infrared properties of certain two dimensional sigma models couples to N=2* gauge theories. This provides strong evidence for the proposed duality between the two descriptions. […]

DISIT-2017YITP-17-68ARC-17-09arXiv:1711.07194JHEP 1805 (2018) 040JHEP 1807 (2018) 175by: Castellani, L. (Piemonte Orientale U., Alessandria) et al.Abstract: We reconstruct the action of $N=1, D=4$ Wess-Zumino and $N=1, 2, D=4$ super-Yang-Mills theories, using integral top forms on the supermanifold ${\cal M}^{(4|4)}$. Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework. […]

arXiv:1711.05530JHEP 1801 (2018) 113by: Gliozzi, Ferdinando (INFN, Turin)Abstract: We compute, to the first non-trivial order in the ϵ-expansion of a perturbed scalar field theory, the anomalous dimensions of an infinite class of primary operators with arbitrary spin ℓ = 0, 1, . . . , including as a particular case the weakly broken higher-spin currents, using only constraints from conformal symmetry. Following the bootstrap philosophy, no reference is made to any Lagrangian, equations of motion or coupling constants. Even the space dimensions d are left free. The interaction is implicitly turned on through the local operators by letting them acquire anomalous dimensions. […]

YITP-17-114ARC-17-10arXiv:1710.11498by: Fré, Pietro (INFN, Turin) et al.Abstract: We consider super Yang-Mills theory on supermanifolds $\mathcal{M}^{(D|m)}$ using integral forms. The latter are used to define a geometric theory of integration and are essential for a consistent action principle. The construction relies on Picture Changing Operators $\mathbb{Y}^{(0|m)}$, analogous to those introduced in String Theory, that admit the geometric interpretation of Poincar\'e duals of closed submanifolds of superspace $\mathcal{S}^{(D|0)} \subset \mathcal{M}^{(D|m)}$ having maximal bosonic dimension $D$. We discuss the case of Super-Yang-Mills theory in $D=10$ with $\mathcal{N}=1$ supersymmetry and we show how to retrieve its pure-spinor formulation from the rheonomic lagrangian $\mathcal{L}_{rheo}$ of D'Auria, Fr\'e and Da Silva, choosing a suitable $\mathbb{Y}^{(0|m)}_{ps}$. From the same lagrangian $\mathcal{L}_{rheo}$, with another choice $\mathbb{Y}^{(0|m)}_{comp}$ of the PCO, one retrieves the component form of the SYM action. Equivalence of the formulations is ensured when the corresponding PCO.s are cohomologous, which is true, in this case, of $\mathbb{Y}^{(0|m)}_{ps}$ and $\mathbb{Y}^{(0|m)}_{comp}$. […]

EMPG-17-16arXiv:1710.11467JHEP 1802 (2018) 036by: Aschieri, Paolo (Piemonte Orientale U., Alessandria) et al.Abstract: We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct preliminary steps towards a nonassociative theory of gravity on spacetime. We obtain explicit expressions for the torsion, curvature, Ricci tensor and Levi-Civita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct R-flux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in non-geometric string theory and double field theory. […]

arXiv:1709.10117JHEP 1802 (2018) 093by: Playle, Sam (INFN, Turin) et al.Abstract: We present an approach to the parametrization of (super) Schottky space obtained by sewing together three-punctured discs with strips. Different cubic ribbon graphs classify distinct sets of pinching parameters, we show how they are mapped onto each other. The parametrization is particularly well-suited to describing the region within (super) moduli space where open bosonic or Neveu-Schwarz string propagators become very long and thin, which dominates the IR behaviour of string theories. We show how worldsheet objects such as the Green’s function converge to graph theoretic objects such as the Symanzik polynomials in the α$^{′}$ → 0 limit, allowing us to see how string theory reproduces the sum over Feynman graphs. The (super) string measure takes on a simple and elegant form when expressed in terms of these parameters. […]

ARC-17-5arXiv:1707.08922JHEP 1711 (2017) 137by: Ashok, S.K. (HBNI, Mumbai) et al.Abstract: We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three dimensions, coupled respectively to four- and five-dimensional gauge theories. The chiral ring equations, which arise from extremizing a twisted chiral superpotential, are solved as power series in the infrared scales of the quiver theories. In the second approach we use equivariant localization and obtain the twisted chiral superpotential as a function of the Coulomb moduli of the four- and five-dimensional gauge theories, and find a perfect match with the results obtained from the chiral ring equations. In the five-dimensional case this match is achieved after solving a number of subtleties in the localization formulas which amounts to choosing a particular residue prescription in the integrals that yield the Nekrasov-like partition functions for ramified instantons. We also comment on the necessity of including Chern-Simons terms in order to match the superpotentials obtained from dual quiver descriptions of a given surface operator. […]

ARC-17-04arXiv:1707.03411JHEP 1710 (2017) 062by: Castellani, Leonardo (Piemonte Orientale U., Alessandria)Abstract: We present an action for chiral N = (1, 0) supergravity in 2 + 2 dimensions. The fields of the theory are organized into an OSp(1|4) connection supermatrix, and are given by the usual vierbein V$^{a}$ , spin connection ω$^{ab}$ , and Majorana gravitino ψ. In analogy with a construction used for D = 10 + 2 gauge supergravity, the action is given by ∫STr(R$^{2}$ Γ), where R is the OSp(1|4) curvature supermatrix two-form, and Γ a constant supermatrix containing γ$_{5}$. It is similar, but not identical to the MacDowell-Mansouri action for D = 2 + 2 supergravity. The constant supermatrix breaks OSp(1|4) gauge invariance to a subalgebra OSp(1|2) ⊕ Sp(2), including a Majorana-Weyl supercharge. Thus half of the OSp(1|4) gauge supersymmetry survives. The gauge fields are the selfdual part of ω$^{ab}$ and the Weyl projection of ψ for OSp(1|2), and the antiselfdual part of ω$^{ab}$ for Sp(2). Supersymmetry transformations, being part of a gauge superalgebra, close off-shell. The selfduality condition on the spin connection can be consistently imposed, and the resulting “projected” action is OSp(1|2) gauge invariant. […]

arXiv:1707.00710JHEP 1710 (2017) 085by: Loukas, Orestis (Bern U.) et al.Abstract: We show that the large-charge formalism can be successfully applied to models that go beyond the vector models discussed so far in the literature. We study the explicit example of a conformal SU(3) matrix model in 2+1 space-time dimensions at fixed charge and calculate the anomalous dimension and fusion coefficients at leading order in the U(1) charge. […]

arXiv:1707.00711Phys.Rev.Lett. 120 (2018) 061603by: Banerjee, Debasish (DESY, Zeuthen) et al.Abstract: We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the O(2) universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global U(1) charge can be obtained via a series expansion in the inverse charge 1/Q. We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series. […]

(A)-DISIT-2017ARC-17-03YITP-17-52arXiv:1706.04704Annales Henri Poincare 19 (2018) 1385-1417by: Castellani, L. (Piemonte Orientale U., Alessandria) et al.Abstract: We reformulate super-quantum mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of picture changing operators (PCO). In this way we retrieve component and superspace actions and prove their equivalence. The PCO are closed integral forms and can be interpreted as super-Poincaré duals of bosonic submanifolds embedded into a supermanifold. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, N=1$ and the $D=1, N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism, we also consider coupling with gauge fields, Hilbert space of quantum states, and observables. […]

arXiv:1705.09297Nucl.Phys. B924 (2017) 153-177by: Amariti, Antonio (Bern U.) et al.Abstract: We present a new family of dualities for three-dimensional gauge theories, motivated by the brane realization of the reduction of four-dimensional dualities on a circle. This family can be understood as a generalization of Aharony duality to quiver gauge theories whose nodes interact via monopole terms in the superpotential. We refer to this family of theories as monopole quivers. We corroborate the new dualities by checking the equivalence of the three-sphere partition functions, obtained from the standard circle reduction of the four-dimensional superconformal index. As a special case, we recover some dualities recently discussed in the literature. […]

arXiv:1705.06251Phys.Lett. B772 (2017) 578-585by: Andrianopoli, Laura (INFN, Turin) et al.Abstract: In this paper we clarify the relations occurring among the osp(1|32) algebra, the M -algebra and the hidden superalgebra underlying the Free Differential Algebra of D=11 supergravity (to which we will refer as DF-algebra) that was introduced in the literature by D'Auria and Frè in 1981 and is actually a (Lorentz valued) central extension of the M -algebra including a nilpotent spinor generator, Q′ . We focus in particular on the 4-form cohomology in 11D superspace of the supergravity theory, strictly related to the presence in the theory of a 3-form A(3) . Once formulated in terms of its hidden superalgebra of 1-forms, we find that A(3) can be decomposed into the sum of two parts having different group-theoretical meaning: One of them allows to reproduce the FDA of the 11D Supergravity due to non-trivial contributions to the 4-form cohomology in superspace, while the second one does not contribute to the 4-form cohomology, being a closed 3-form in the vacuum, defining however a one parameter family of trilinear forms invariant under a symmetry algebra related to osp(1|32) by redefining the spin connection and adding a new Maurer–Cartan equation. […]

arXiv:1705.02909Nucl.Phys. B926 (2018) 427-466by: Billo, M. (INFN, Turin) et al.Abstract: We consider two-point correlators in SU( N ) gauge theories on R4 with N=2 supersymmetry and Nf massless hypermultiplets in the fundamental representation. Using localization on S4 , we compute the leading perturbative corrections to the two-point functions of chiral/anti-chiral operators made of scalar fields. The results are compared at two and three loops against direct field theory computations for some special operators whose correlators remain finite in perturbation theory at the specific loop order. In the conformal case, the match is shown up to two loops for a generic choice of operators and for arbitrary N . […]

ARC-17-01YITP-17-48arXiv:1705.00752Fortsch.Phys. 65 (2017) 1700040by: Fré, P. (INFN, Turin) et al.Abstract: We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS4/CFT3 correspondence. From the structural view-point, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kähler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS4/CFT3 correspondence and more generally of M2-branes we emphasize the role of the Kähler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non-compact Kähler quotient K4 of some flat variety with respect to a suitable group. The crepant resolutions of Cn/Γ singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern-Simons Theory supposedly dual to the corresponding M2-brane solution. […]

ARC-17-02arXiv:1705.00638JHEP 1706 (2017) 061by: Castellani, Leonardo (Turin U.)Abstract: We present an action for N = 1 supergravity in 10 + 2 dimensions, containing the gauge fields of the OSp(1|64) superalgebra, i.e. one-forms B$^{(}^{n}^{)}$ with n=1,2,5,6,9,10 antisymmetric D=12 Lorentz indices and a Majorana gravitino ψ. The vielbein and spin connection correspond to B$^{(1)}$ and B$^{(2)}$ respectively. The action is not gauge invariant under the full OSp(1|64) superalgebra, but only under a subalgebra $ \tilde{F} $ (containing the F algebra OSp(1|32)), whose gauge fields are B$^{(2)}$, B$^{(6)}$, B$^{(10)}$ and the Weyl projected Majorana gravitino $ \frac{1}{2}\left(1+{\Gamma}_{13}\right)\psi $ . Supersymmetry transformations are therefore generated by a Majorana-Weyl supercharge and, being part of a gauge superalgebra, close off-shell. The action is simply ∫STr(R$^{6}$ Γ) where R is the OSp(1|64) curvature supermatrix two-form, and Γ is a constant supermatrix involving Γ$_{13}$ and breaking OSp(1|64) to its $ \tilde{F} $ subalgebra. The usual Einstein-Hilbert term is included in the action. […]

arXiv:1703.08726JHEP 1710 (2017) 152by: Aschieri, Paolo (INFN, Turin) et al.Abstract: We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. […]

arXiv:1702.06489Eur.Phys.J. C77 (2017) 806by: Larocca, Pier Vittorio (INFN, Turin) et al.Abstract: Starting from the pseudo- ${\mathcal {B}}_0$ gauge solution for marginal deformations in OSFT, we analytically compute the relation between the perturbative deformation parameter $\tilde{\lambda }$ in the solution and the BCFT marginal parameter $\lambda $ , up to fifth order, by evaluating the Ellwood invariants. We observe that the microscopic reason why $\tilde{\lambda }$ and $\lambda $ are different is that the OSFT propagator renormalizes contact-term divergences differently from the contour deformation used in BCFT. […]

CERN-TH-2017-038arXiv:1702.04998Nucl.Phys. B923 (2017) 32-53by: Angelantonj, Carlo (INFN, Turin) et al.Abstract: The N=2⁎ supersymmetric gauge theory is a massive deformation of N=4 , in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian N=2⁎ theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N=2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω -background, in agreement with a recent proposal. […]

CALT-TH-2017-009arXiv:1702.03938JHEP 1704 (2017) 056by: Gliozzi, Ferdinando (Turin U.) et al.Abstract: We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ϵ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O(N)-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned. […]

arXiv:1702.02833JHEP 1707 (2017) 068by: Ashok, S.K. (HBNI, Mumbai) et al.Abstract: We calculate the instanton partition function of the four-dimensional $ \mathcal{N}={2}^{\star } $ SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure $ \mathcal{N}=2 $ or to $ \mathcal{N}={2}^{\star } $ gauge theories. […]

LAPTH-001-17arXiv:1701.07855Nucl.Phys. B918 (2017) 129-161by: Pesando, Igor (Annecy, LAPTH)Abstract: String theory gives S matrix elements from which is not possible to read any gauge information. Using factorization we go off shell in the simplest and most naive way and we read which are the vertices suggested by string. To compare with the associated Effective Field Theory it is natural to use color ordered vertices. The α′=0 color ordered vertices suggested by string theory are more efficient than the usual ones since the three gluon color ordered vertex has three terms instead of six and the four gluon one has one term instead of three. They are written in the so called Gervais–Neveu gauge. The full Effective Field Theory is in a generalization of the Gervais–Neveu gauge with α′ corrections. Moreover a field redefinition is required to be mapped to the field used by string theory. […]