Twisted S-Duality

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.