Topological D-branes from Descent

TL;DR

This paper generalizes the coupling of the open topological B-model to holomorphic vector bundles by introducing graded bundles with superconnections, linking to derived category objects.

Contribution

It extends the boundary coupling construction to graded bundles with superconnections, connecting topological strings to derived category objects.

Findings

Derived category objects correspond to generalized boundary conditions.

Open string vertex operators are computed for graded bundles with superconnections.

The construction unifies topological D-branes with derived category formalism.

Abstract

Witten couples the open topological B-model to a holomorphic vector bundle by adding to the boundary of the worldsheet a Wilson loop for an integrable connection on the bundle. Using the descent procedure for boundary vertex operators in this context, I generalize this construction to write a worldsheet coupling for a graded vector bundle with an integrable superconnection. I then compute the open string vertex operators between two such boundaries. A theorem of J. Block gives that this is equivalent to coupling the B-model to an arbitrary object in the derived category.