Enhanced D-Brane Categories from String Field Theory

TL;DR

This paper constructs D-brane categories in B-type topological string theory using string field equations and superconnections, linking string field theory with derived categories and revealing non-holomorphic deformations.

Contribution

It introduces a novel approach to D-brane categories via string field solutions and superconnections, connecting with established mathematical frameworks.

Findings

D-brane categories are realized as solutions to string field equations.

The construction relates to Bondal and Kapranov's work.

Non-holomorphic deformations are incorporated unexpectedly.

Abstract

We construct D-brane categories in B-type topological string theory as solutions to string field equations of motion. Using the formalism of superconnections, we show that these solutions form a variant of a construction of Bondal and Kapranov. This analysis is an elaboration on recent work of Lazaroiu. We also comment on the relation between string field theory and the derived category approach of Douglas, and Aspinwall and Lawrence. Non-holomorphic deformations make a somewhat unexpected appearance in this construction.