Mirror symmetry for topological sigma models with generalized Kahler geometry

TL;DR

This work constructs an explicit mirror map $\mathcal{M}$ for topological sigma models with generalized Kahler target spaces and demonstrates that generalized A- and B-models are mirror pairs, with observables, instantons, and anomalies consistently mapped. The analysis uses the pure spinor and maximal isotropic formalism of generalized geometry, showing that $\mathcal{M}$ exchanges the two generalized complex structures $\mathcal{J}_1$ and $\mathcal{J}_2$ and maps $(I_+,I_-)\to (I_+, -I_-)$, effectively implementing a T-duality along a $T^3$ fibre in a torus-fibered $M^6$. The brane sector reveals that A-branes map to B-branes under $\mathcal{M}$, and the worldvolume two-form $F$ on the brane translates into a mirror bivector $\beta$, signaling a noncommutative deformation on the mirror manifold and connecting to $B$-transformations in generalized geometry. Overall, the paper provides a concrete, geometrically grounded framework for understanding mirror symmetry in the generalized Kahler setting and its implications for branes and noncommutative structures.

Abstract

We consider topological sigma models with generalized Kahler target spaces. The mirror map is constructed explicitly for a special class of target spaces and the topological A and B model are shown to be mirror pairs in the sense that the observables, the instantons and the anomalies are mapped to each other. We also apply the construction to open topological models and show that A branes are mapped to B branes. Furthermore, we demonstrate a relation between the field strength on the brane and a two-vector on the mirror manifold.