Twisted S-Duality
Surya Raghavendran, Philsang Yoo
TL;DR
This work builds a mathematical framework for S-duality as an $SL(2,\mathbb{Z})$ action on a twisted sector of type IIB supergravity, realized through a modified BCOV theory in three complex dimensions. It establishes a robust link between twisted BCOV/BCOV-like theories, twisted IIB supergravity, and the dualities that arise from dimensional reductions and T-duality, culminating in an $SL(2,\mathbb{Z})$–equivariant map from 11d twisted supergravity to twisted IIB; this ties duality actions to geometric Langlands across deformations of holomorphic–topological gauges theories. The paper then applies this framework to deformations of Kapustin’s holomorphic–topological twist of $\mathcal{N}=4$ theory, D3-brane gauge theories, and the Dolbeault/de Rham Langlands correspondences, showing how S-duality pairs HT(A) and HT(B) deformations and yields new perspectives on geometric Langlands via boundary conditions and open–closed maps. It also develops a detailed web of dualities involving M-theory, T-duality, and reductions, and demonstrates how twisted S-duality interacts with superconformal symmetries and 4d Chern–Simons theory, offering a mathematically tractable route to many string-theoretic dualities with far-reaching implications for representation theory and nonperturbative invariants.
Abstract
We study an SL(2, Z) symmetry of a variant of BCOV theory in three complex dimensions. Using conjectural descriptions of twists of superstrings in terms of topological strings, we argue that this action can be thought of as a version of S-duality that preserves an SU(3)-invariant twist of type IIB supergravity. We analyze how SL(2,Z) acts on various deformations of the holomorphic-topological twist of 4-dimensional N = 4 supersymmetric gauge theory, which come from residual supertranslations and superconformal symmetries, and are of relevance to geometric Langlands theory and gauge-theoretic constructions of the Yangian.