Supersymmetric Topological Sigma Models and Doubling Spaces

TL;DR

This paper explores the topological B-model on complex tori within a doubled geometry framework, revealing new insights into D-branes, T-duality, and the derived category through geometric symmetry and intersection theory.

Contribution

It introduces a novel method using doubled geometry to analyze the B-model on tori, incorporating rank-one D-branes and connecting intersection theory with BRST cohomology.

Findings

Lifted branes' intersection theory computes BRST cohomology

T-duality acts as a geometric symmetry in doubled space

New perspective on derived categories of tori

Abstract

Witten's topological B-model on a Calabi-Yau background is known to reproduce, in the open string sector, the derived category of coherent sheaves. When the target space is a complex torus, the topological model enjoys a non-geometric symmetry known as T-duality, which relates the theories on the torus and dual torus backgrounds. By considering the "double field theory" of Hull and Reid-Edwards on the product of a torus and its dual, T-duality occurs as a geometric symmetry of the target space. Building on the methods of Y. Qin, we propose a method of analyzing the topological B-model on a torus in the doubled geometry framework which naturally incorporates certain rank-one D-branes, providing a different perspective on the derived category of the torus. In certain cases, the intersection theory of these lifted branes correctly computes the BRST cohomology of the B-model, and hence the derived Hom-spaces of the corresponding line bundles.