D-branes, B fields, and Ext groups

TL;DR

This paper extends the calculation of massless boundary Ramond sector spectra of open strings to include nonzero flat B fields, showing that D-branes are modeled by twisted sheaves and their spectra are counted by Ext groups of these twisted sheaves.

Contribution

It introduces the use of twisted sheaves to model D-branes with nonzero B fields and extends the Ext group counting method to this new setting.

Findings

Massless boundary Ramond sector states are counted by Ext groups of twisted sheaves.

Spectral sequences are used to compute BRST cohomology in this context.

Subtleties from previous work also appear in this extension.

Abstract

In this paper we extend previous work on calculating massless boundary Ramond sector spectra of open strings to include cases with nonzero flat B fields. In such cases, D-branes are no longer well-modelled precisely by sheaves, but rather they are replaced by `twisted' sheaves, reflecting the fact that gauge transformations of the B field act as affine translations of the Chan-Paton factors. As in previous work, we find that the massless boundary Ramond sector states are counted by Ext groups -- this time, Ext groups of twisted sheaves. As before, the computation of BRST cohomology relies on physically realizing some spectral sequences. Subtleties that cropped up in previous work also appear here.