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  • Superstring Field Theory, Superforms and Supergeometry
    by Catenacci, R. on 26 July 2018 at 3:33

    arXiv:1807.09563DISIT-18ARC-18-05by: 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. […]

  • 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 half-BPS surface operators in four dimensional N=2 SU(N) gauge theories. We calculate the ramified instanton partition function using equivariant localization and extract the low-energy 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 Fayet-Iliopoulos parameters of the two dimensional gauge nodes and by the signs of their beta-functions. 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 (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. […]

  • Killing spinors from classical $r$-matrices
    by Orlando, Domenico on 4 May 2018 at 2:03

    arXiv:1805.00948KUNS-2731by: Orlando, Domenico (INFN, Turin) et al.Abstract: The Yang-Baxter (YB) deformation is a systematic way of performibg integrable deformations of two-dimensional 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 $\mathrm{AdS}_5\times S^5$. In this case, a simple class of YB deformation is associated with TsT transformations of string backgrounds. The data of this transformation is encoded in an antisymmetric bi-vector $\Theta$ (which is often called $\beta$ 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 $\Theta$. We moreover discuss the M-theory equivalent of the TsT transformation, allowing us to also give Killing spinors of 11-dimensional backgrounds. We discuss examples of TsT transformed backgrounds starting from flat space, $\mathrm{AdS}_{5}\times S^5$ and $\mathrm{AdS}_{7}\times S^4$. We find that in this way we can relate the $\Omega$-deformation to YB deformations. […]

  • An AdS/EFT correspondence at large charge
    by Loukas, Orestis on 13 April 2018 at 2:47

    arXiv:1804.04151by: 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. In this work we discuss the AdS/CFT correspondence in the regime $Q \gg C_T \gg 1$ where both the EFT and gravity descriptions are valid and stable ($C_T$ being the central charge). We present the observation that the ground state energy as a function of the Abelian charge $Q$ for a simple EFT in some three-dimensional CFT coincides with the expression for the mass of an anti-de Sitter-Reissner-Nordstr\"om black hole as a function of its charge. This observation allows us to introduce a dictionary relating CFT, EFT and holographic descriptions. We also find agreement for the higher-derivative corrections on both sides, suggesting a large-$C_T$ expansion on the EFT side. […]

  • Universal correlation functions in rank 1 SCFTs
    by Hellerman, Simeon on 6 April 2018 at 2:45

    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 $|x - y|$. […]

  • $N=2^∗$ (non-)Abelian theory in the $\Omega$ background from string theory
    by Samsonyan, Marine on 29 March 2018 at 10:13

    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. […]

  • 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 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. […]

  • Correlators between Wilson loop and chiral operators in $ \mathcal{N}=2 $ conformal gauge theories
    by Billo, M. on 28 February 2018 at 3:21

    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. […]

  • Supergravity in the group-geometric framework: a primer
    by Castellani, Leonardo on 13 February 2018 at 3:19

    ARC-18-02arXiv:1802.03407Fortsch.Phys. 66 (2018) 040014by: 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 $d=3,4$ off-shell supergravities and $d=5$ Chern-Simons 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(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. […]

  • 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 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. […]

  • String Sigma Models on Curved Supermanifolds
    by Catenacci, Roberto on 16 January 2018 at 4:58

    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 $E$. […]

  • Surface operators in 5d gauge theories and duality relations
    by Ashok, S.K. on 20 December 2017 at 5:57

    ARC-17-12arXiv:1712.06946JHEP 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. […]

  • Non-Perturbative 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 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. […]

  • Wess-Zumino and Super Yang-Mills Theories in D=4 Integral Superspace
    by Castellani, L. on 21 November 2017 at 5:10

    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. […]

  • 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 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. […]

  • $\mathrm{D=10}$ Super-Yang-Mills Theory and Poincar\'e Duality in Supermanifolds
    by Fré, Pietro on 1 November 2017 at 5:48

    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 $\mathbb{Y}^{(0|m)}_{comp}$. […]

  • Nonassociative differential geometry and gravity with non-geometric fluxes
    by Aschieri, Paolo on 1 November 2017 at 5:48

    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. […]

  • 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 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. […]

  • Surface operators, chiral rings and localization in $ \mathcal{N} $ =2 gauge theories
    by Ashok, S.K. on 28 July 2017 at 3:55

    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. […]

  • Gauge supergravity in D = 2 + 2
    by Castellani, Leonardo on 13 July 2017 at 4:16

    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. […]

  • Matrix models at large charge
    by Loukas, Orestis on 5 July 2017 at 4:17

    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. […]

  • Conformal dimensions via large charge expansion
    by Banerjee, Debasish on 5 July 2017 at 4:13

    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. […]

  • Super Quantum Mechanics in the Integral Form Formalism
    by Castellani, L. on 16 June 2017 at 4:15

    (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. […]