We derive the exact S-matrix for the scattering of particular representations of the centrally-extended psu(1|1) 2 Lie superalgebra, conjectured to be related to the massive modes of the light-cone gauge string theory on AdS 2 × S 2 × T 6 . The S-matrix consists of two copies of a centrally-extended psu(1|1) invariant S-matrix and is in agreement with the tree-level result following from perturbation theory. Although the overall factor is left unfixed, the constraints following from crossing symmetry and unitarity are given. The scattering involves long representations of the symmetry algebra, and the relevant representation theory is studied in detail. We also discuss Yangian symmetry and find it has a standard form for a particular limit of the aforementioned representations. This has a natural interpretation as the massless limit, and we investigate the corresponding limits of the massive S-matrix. Under the assumption that the massless modes of the light-cone gauge string theory transform in these limiting representations, the resulting S-matrices would provide the building blocks for the full S-matrix. Finally, some brief comments are given on the Bethe ansatz.

We propose the γ-deformation of four-dimensional N = 2 quiver gauge theories, obtained by applying the Lunin-Maldacena deformation with respect to the U (1)r × SU (2)R R-symmetry. The resulting theory is supplied with double-trace counterterms and has a non-trivial RG-flow. We compute the one-loop β-function and identify the conformal fixed points of these theories. Furthermore, we study the double-scaling limit of large imaginary γ and weak 't Hooft coupling. In this regime, both gauge fields and hypermultiplets decouple, leaving a non-supersymmetric, non-gauge theory where gluinos and vector multiplet scalars interact via Yukawa couplings. This model is integrable even though the original N = 2 theory is not. Indeed, the anomalous dimension of the BMN vacuum is dominated by fermionic wheel graphs, whose bulk constitutes an integrable fishnet known as brick-wall domain. Finally, we compute this scaling dimension to leading order directly from Feynman diagrams both for the general γ-deformation and the double-scaled theory.

We consider 4d N = 1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robin-like. We show that different boundary conditions are related to each other by coupling the bulk to 3d N = 1 degrees of freedom on the boundary three-torus, for which we derive explicit 1-loop determinants.

Abstract:We verify the self-duality of Green-Schwarz supercoset sigma models on AdS d × S d backgrounds (d = 2, 3, 5) under combined bosonic and fermionic T-dualities without gauge fixing kappa symmetry. We also prove this property for superstrings on AdS d × S d × S d (d = 2, 3) described by supercoset sigma models with the isometries governed by the exceptional Lie supergroups D(2, 1; α) (d = 2) and D(2, 1; α) × D(2, 1; α) (d = 3), which requires an additional T-dualisation along one of the spheres. Then, by taking into account the contribution of non-supercoset fermionic modes (up to the second order), we provide evidence for the T-self-duality of the complete type IIA and IIB Green-Schwarz superstring theory on AdS d × S d × T 10−2d (d = 2, 3) backgrounds with Ramond-Ramond fluxes. Finally, applying the Buscher-like rules to T-dualising supergravity fields, we prove the T-self-duality of the whole class of the AdS d × S d × M 10−2d superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.

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