Enhanced d-brane categories from string field theory

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 an enhanced triangulated category as defined by 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.