We present a correspondence between two-dimensional \mathcal{N} = (2,2)𝒩=(2,2) supersymmetric gauge theories and rational integrable \mathfrak{gl}(m|n)𝔤𝔩(m|n) spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern–Simons theory with gauge group GL(m|n)GL(m|n). The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational \mathfrak{gl}(m|n)𝔤𝔩(m|n) spin chains with spins valued in finite-dimensional representations.

We present a correspondence between two-dimensional N = (2, 2) supersymmetric gauge theories and rational integrable gl(m|n) spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern-Simons theory with gauge group GL(m|n). The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational gl(m|n) spin chains with spins valued in finite-dimensional representations. A Four-dimensional Chern-Simons theory with gauge supergroup from twisted string theory 51 A.1 Topological strings 52 A.2 Topological open string field theory 53 A.3 Twisted closed string field theory 55 A.4 Closed-open map 56 A.5 Four-dimensional Chern-Simons theory with gauge supergroup from the SU(3)-invariant twist of type IIB string theory 58

S-duality is a nontrivial self-duality of type IIB string theory that exchanges strong and weak coupling. We give a mathematically rigorous description of how S-duality acts on a low-energy supersymmetry-protected sector of IIB string theory, using a conjectural description of such protected sectors in terms of topological string theory. We then give some applications which are of relevance to Geometric Langlands Theory and the representation theory of the Yangian.

We construct a fully interacting holomorphic/topological theory in eleven dimensions that is defined on products of Calabi-Yau fivefolds with real one-manifolds. The theory describes a particular deformation of the cotangent bundle to the moduli space of Calabi-Yau structures on the fivefold. Its field content matches the holomorphic (or minimal) twist of the eleven-dimensional supergravity multiplet recently computed by the second two authors, and we offer numerous consistency checks showing that the interactions correctly describe interacting twisted eleven-dimensional supergravity at the perturbative level. We prove that the global symmetry algebra of our model on flat space is an L8 central extension of the infinitedimensional simple exceptional super Lie algebra Ep5, 10q, following a recent suggestion of Cederwall in the context of the relevant pure spinor model. Twists of superconformal algebras map to the fields of our model on the complement of a stack of M2 or M5 branes, laying the groundwork for a fully holomorphic version of twisted holography in this context.