Stability Conditions For Topological D-branes: A Worldsheet Approach

TL;DR

The paper derives worldsheet SUSY conditions for topological D-branes of types A and B by enforcing spectral flow matching in an N=2 superconformal boundary. It shows B-brane stability conditions reproduce known MMMS results and extend to non-flat gauge fields, while A-brane stability requires coisotropic geometry and a complex-structure condition on the reduced flux, connecting to special Lagrangian cases. The authors introduce a generalized Maslov class and a grading for coisotropic A-branes, proposing a path toward coisotropic Floer-type theories for open strings. Overall, the work unifies worldsheet and Born-Infeld perspectives and broadens stability notions beyond special Lagrangian settings with implications for mirror symmetry and topological string theory.

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.