Stability Conditions For Topological D-branes: A Worldsheet Approach

TL;DR

This paper derives stability conditions for topological A- and B-branes using a worldsheet approach, reproducing known results and introducing new conditions for coisotropic A-branes, with implications for Floer homology.

Contribution

It provides a worldsheet-based derivation of stability conditions for topological D-branes, including new conditions for coisotropic A-branes and a framework for their grading and Floer homology.

Findings

Reproduces known stability conditions for A- and B-branes.

Introduces new stability conditions for coisotropic A-branes.

Defines an analogue of the Maslov class and grading for coisotropic A-branes.

Abstract

We study conditions on the topological D-branes of types A and B obtained by requiring a proper matching of the spectral flow operators on the boundary. These conditions ensure space-time supersymmetry and stability of D-branes. In most cases, we reproduce the results of Marino-Minasian-Moore-Strominger, who studied the same problem using the supersymmetric Born-Infeld action. In some other cases, corresponding to coisotropic A-branes, our stability condition is new. Our results enable us to define an analogue of the Maslov class and grading for coisotropic A-branes. We expect that they play a role in a conjectural generalization of the Floer homology.