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History operators in quantum mechanics
by Castellani, Leonardo on 12 October 2018 at 2:08
arXiv:1810.03624ARC1806by: 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 pathintegral. 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 twovector formalism in the case of given initial and final states. We apply the history operator formalism to a few examples: entangler circuit, MachZehnder interferometer, teleportation circuit. Not surprisingly, the propagation of coordinate eigenstates $q\rangle$ is described by a history operator $C$ containing the Feynman pathintegral. […]

The largecharge expansion for Schrödinger systems
by Favrod, Samuel on 19 September 2018 at 2:21
arXiv:1809.06371by: Favrod, Samuel (Zurich, ETH) et al.Abstract: In this note, we perform the largecharge expansion for nonrelativistic systems with a global $U(1)$ symmetry in $3+1$ and $2+1$ spacetime 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 lowenergy 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 largecharge expansion in which quantum corrections are suppressed with respect to the nexttoleading order terms in the Lagrangian. We give the nexttoleadingorder expressions for the ground state energy and the speed of sound. […]

Global SeibergWitten maps for $U(n)$bundles on tori and Tduality
by Aschieri, Paolo on 18 September 2018 at 9:34
arXiv:1809.05426by: Aschieri, Paolo (Piemonte Orientale U., Alessandria) et al.Abstract: SeibergWitten maps are a wellestablished 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, SeibergWitten maps provide a quantization of bundles with connections. We study the case of U(n)vector bundles on twodimensional tori, prove the existence of globally defined SeibergWitten maps (induced from the plane to the torus) and show their compatibility with Morita equivalence. […]

Superstring Field Theory, Superforms and Supergeometry
by Catenacci, R. on 26 July 2018 at 3:33
arXiv:1807.09563DISIT18ARC1805by: 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 sheaftheoretical 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. […]

Surface operators, dual quivers and contours
by Ashok, S.K. on 18 July 2018 at 2:24
arXiv:1807.06316by: Ashok, S.K. (IMSc, Chennai) et al.Abstract: We study halfBPS surface operators in four dimensional N=2 SU(N) gauge theories. We calculate the ramified instanton partition function using equivariant localization and extract the lowenergy effective action on the four dimensional Coulomb branch. 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 relative magnitudes of the FayetIliopoulos parameters of the two dimensional gauge nodes and by the signs of their betafunctions. 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. […]

The Gauge Group of a Noncommutative Principal Bundle and Twist Deformations
by Aschieri, Paolo on 6 June 2018 at 15:50
arXiv:1806.01841by: Aschieri, PaoloAbstract: We study noncommutative principal bundles (HopfGalois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasicommutative, 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 (2cocycle) deformations of HopfGalois 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. […]

Killing spinors from classical $r$matrices
by Orlando, Domenico on 4 May 2018 at 2:03
arXiv:1805.00948KUNS2731J.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 nonlinear sigma models. The deformations can be labeled by classical rmatrices 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 bivector Θ (which is often called β field or noncommutativity 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 Mtheory 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 Ωdeformation to yb deformations. […]

An AdS/EFT correspondence at large charge
by Loukas, Orestis on 13 April 2018 at 2:47
arXiv:1804.04151Nucl.Phys. B934 (2018) 437458by: 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 stronglycoupled 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. […]

Universal correlation functions in rank 1 SCFTs
by Hellerman, Simeon on 6 April 2018 at 2:45
arXiv:1804.01535CALTTH2018014IPMU180059by: 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 powerlaw corrections to the twopoint 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 fourdimensional $\mathcal{N} =2$ 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 theorydependent coefficients, $\alpha$ is the coefficient of the WessZumino 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 Coulombbranch effective field theory (EFT) with the supersymmetric recursion relations. However, our results constrain the powerlaw corrections to all orders, even for nonLagrangian 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 doublescaling 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 $x  y$. […]

$N=2^∗$ (non)Abelian theory in the $\Omega$ background from string theory
by Samsonyan, Marine on 29 March 2018 at 10:13
PoS EPSHEP2017 (2017) 546by: Samsonyan, Marine (CERN) et al.Abstract: We present a Dbrane realisation of the Abelian and nonAbelian 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. […]

Extended Gauge Theory Deformations From~Flux~Backgrounds
by Lambert, Neil on 19 March 2018 at 2:39
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 Rsymmetry into the gauge symmetry. Furthermore we construct higherorder generalisations, also expressed a twisting of the Rsymmetry, that have symmetries associated to codimension two and three defects. […]

Correlators between Wilson loop and chiral operators in $ \mathcal{N}=2 $ conformal gauge theories
by Billo, M. on 28 February 2018 at 3:21
ARC1803arXiv:1802.09813JHEP 1803 (2018) 193by: Billo, M. (Turin U.) et al.Abstract: We consider conformal N=2 super YangMills theories with gauge group SU(N) and Nf=2N fundamental hypermultiplets in presence of a circular 1/2BPS Wilson loop. It is natural to conjecture that the matrix model which describes the expectation value of this system also encodes the onepoint 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 twoloop order, the onepoint functions computed in field theory with the vacuum expectation values of the corresponding normalordered operators in the matrix model. For the part of these expressions with transcendentality zeta(3), we also obtain results in the largeN limit that are exact in the 't Hooft coupling lambda. […]

Supergravity in the groupgeometric framework: a primer
by Castellani, Leonardo on 13 February 2018 at 3:19
ARC1802arXiv:1802.03407Fortsch.Phys. 66 (2018) 040014by: Castellani, Leonardo (Piemonte Orientale U., Alessandria)Abstract: We review the groupgeometric 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 $d=3,4$ offshell supergravities and $d=5$ ChernSimons supergravity are discussed in detail. A cursory account of $d=10+2$ 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 $d=s+t$ dimensions are summarized in Appendices. […]

Unconventional supersymmetry at the boundary of AdS$_{4}$ supergravity
by Andrianopoli, L. on 25 January 2018 at 5:15
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(22) x SO(1,2) invariance and is shown to contain the D=3 superChern Simons OSp(22) theory considered in [Alvarez:2011gd] and featuring "unconventional local supersymmetry". The model constructed in that reference describes the dynamics of a spin1/2 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 spin1/2 fermion originates from the radial components of the gravitini in D=4. […]

Localization of effective actions in open superstring field theory
by Maccaferri, Carlo on 24 January 2018 at 2:21
arXiv:1801.07607JHEP 1803 (2018) 112by: Maccaferri, Carlo (INFN, Turin) et al.Abstract: We consider the construction of the algebraic part of Dbranes treelevel 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 twopoint functions. As examples of this general mechanism, we show how the YangMills quartic potential and the instanton effective action of a Dp/D(p − 4) system are reproduced. […]

String Sigma Models on Curved Supermanifolds
by Catenacci, Roberto on 16 January 2018 at 4:58
ARC1801arXiv: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 $E$. […]

Surface operators in 5d gauge theories and duality relations
by Ashok, S.K. on 20 December 2017 at 5:57
ARC1712arXiv:1712.06946JHEP 1805 (2018) 046by: Ashok, S.K. (IMSc, Chennai) et al.Abstract: We study halfBPS 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 ChernSimons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the ChernSimons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by AharonySeiberg dualities. […]

NonPerturbative aspects of Supersymmetric Gauge Theories with surface operators
by Rajan John, Renjan on 19 December 2017 at 6:38
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 bifundamental representations, such that at each node the betafunction vanishes. To compute the prepotential for these theories, we follow three different approaches. These are (i) the classic SeibergWitten approach, in which we consider an Mtheory construction of the SeibergWitten 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 nonlocal operators that have support on a two dimensional submanifold of the four dimensional spacetime. They are defined by the singularities they induce in the fourdimensional gauge fields, or can be characterized by the twodimensional theory they support on their worldvolume. The infrared dynamics on the worldvolume of the twodimensional 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 Sduality, 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 fourdimensional 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. […]

WessZumino and Super YangMills Theories in D=4 Integral Superspace
by Castellani, L. on 21 November 2017 at 5:10
DISIT2017YITP1768ARC1709arXiv:1711.07194JHEP 1805 (2018) 040JHEP 1807 (2018) 175by: Castellani, L. (Piemonte Orientale U., Alessandria) et al.Abstract: We reconstruct the action of $N=1, D=4$ WessZumino and $N=1, 2, D=4$ superYangMills theories, using integral top forms on the supermanifold ${\cal M}^{(44)}$. 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. […]

Anomalous dimensions of spinning operators from conformal symmetry
by Gliozzi, Ferdinando on 16 November 2017 at 7:23
arXiv:1711.05530JHEP 1801 (2018) 113by: Gliozzi, Ferdinando (INFN, Turin)Abstract: We compute, to the first nontrivial order in the ϵexpansion 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 higherspin 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. […]

$\mathrm{D=10}$ SuperYangMills Theory and Poincar\'e Duality in Supermanifolds
by Fré, Pietro on 1 November 2017 at 5:48
YITP17114ARC1710arXiv:1710.11498by: Fré, Pietro (INFN, Turin) et al.Abstract: We consider super YangMills theory on supermanifolds $\mathcal{M}^{(Dm)}$ 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 $\mathbb{Y}^{(0m)}$, analogous to those introduced in String Theory, that admit the geometric interpretation of Poincar\'e duals of closed submanifolds of superspace $\mathcal{S}^{(D0)} \subset \mathcal{M}^{(Dm)}$ having maximal bosonic dimension $D$. We discuss the case of SuperYangMills theory in $D=10$ with $\mathcal{N}=1$ supersymmetry and we show how to retrieve its purespinor formulation from the rheonomic lagrangian $\mathcal{L}_{rheo}$ of D'Auria, Fr\'e and Da Silva, choosing a suitable $\mathbb{Y}^{(0m)}_{ps}$. From the same lagrangian $\mathcal{L}_{rheo}$, with another choice $\mathbb{Y}^{(0m)}_{comp}$ 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 $\mathbb{Y}^{(0m)}_{ps}$ and $\mathbb{Y}^{(0m)}_{comp}$. […]

Nonassociative differential geometry and gravity with nongeometric fluxes
by Aschieri, Paolo on 1 November 2017 at 5:48
EMPG1716arXiv: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 nongeometric 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 LeviCivita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct Rflux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in nongeometric string theory and double field theory. […]

Pinching parameters for open (super) strings
by Playle, Sam on 2 October 2017 at 3:27
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 threepunctured 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 wellsuited to describing the region within (super) moduli space where open bosonic or NeveuSchwarz 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. […]

Surface operators, chiral rings and localization in $ \mathcal{N} $ =2 gauge theories
by Ashok, S.K. on 28 July 2017 at 3:55
ARC175arXiv:1707.08922JHEP 1711 (2017) 137by: Ashok, S.K. (HBNI, Mumbai) et al.Abstract: We study halfBPS 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 fivedimensional 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 fivedimensional gauge theories, and find a perfect match with the results obtained from the chiral ring equations. In the fivedimensional 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 Nekrasovlike partition functions for ramified instantons. We also comment on the necessity of including ChernSimons terms in order to match the superpotentials obtained from dual quiver descriptions of a given surface operator. […]

Gauge supergravity in D = 2 + 2
by Castellani, Leonardo on 13 July 2017 at 4:16
ARC1704arXiv: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(14) 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(14) curvature supermatrix twoform, and Γ a constant supermatrix containing γ$_{5}$. It is similar, but not identical to the MacDowellMansouri action for D = 2 + 2 supergravity. The constant supermatrix breaks OSp(14) gauge invariance to a subalgebra OSp(12) ⊕ Sp(2), including a MajoranaWeyl supercharge. Thus half of the OSp(14) gauge supersymmetry survives. The gauge fields are the selfdual part of ω$^{ab}$ and the Weyl projection of ψ for OSp(12), and the antiselfdual part of ω$^{ab}$ for Sp(2). Supersymmetry transformations, being part of a gauge superalgebra, close offshell. The selfduality condition on the spin connection can be consistently imposed, and the resulting “projected” action is OSp(12) gauge invariant. […]