Double field theory for the A/B-models and topological S-duality in generalized geometry

Abstract

We study AKSZ-type BV constructions for the topological A- and B-models within a double field theory formulation that incorporates backgrounds with geometric and non-geometric fluxes. We relate them to a Courant sigma-model, on an open membrane, corresponding to a generalized complex structure, which reduces to the A- or B-models on the boundary. We introduce S-duality at the level of the membrane sigma-model based on the generalized complex structure, which exchanges the related AKSZ field theories, and interpret it as topological S-duality of the A- and B-models. Our approach leads to new classes of Courant algebroids associated to (generalized) complex geometry.

arXiv comment39 pages, 1 figure; v2: typos corrected, reference added

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• BRST symmetry of doubled membrane sigma-models
• Basic curvature and the Atiyah cocycle in gauge theory
• A topological quantum field theory for $\mathrm{Spin}(7)$-instantons