B-branes and the Derived Category

TL;DR

This paper compares the spectrum of the topological B-model with Ext groups of sheaves, revealing the necessity of twisting vector bundles by the canonical Spin^c structure for accurate physical brane descriptions.

Contribution

It establishes a direct link between CFT computations of the B-model spectrum and Ext groups, highlighting the importance of Spin^c twisting in the mathematical description of B-branes.

Findings

Spectrum matches Ext groups when bundles are twisted by Spin^c structures.

Demonstrates the role of canonical Spin^c structures in physical brane descriptions.

Provides a mathematical framework connecting CFT results with derived categories.

Abstract

By a direct CFT computation, the spectrum of the topological B-model is compared to Ext groups of sheaves. A match can only be made if abstract vector bundles on holomorphic submanifolds are twisted by the canonical $\mathrm{Spin}^c$ structure of its support in describing physical branes.