Abstract:

We start with topological sigma-models called the A-model and the B-model whose target spaces are symplectic or Calabi-Yau manifolds. When the worldsheet has a non-empty boundary, the boundary conditions of the sigma-models are specified by branes. Supersymmetry requires that the branes are A-branes supported on Lagrangian or coisotropic submanifolds and B-branes supported on complex submanifolds. We also discuss the A-infinity structure that appears in the category of branes. We then consider sigma-models whose target spaces are generalised Calabi-Yau manifolds with 3-form fluxes, and the B-field transforms among them. If time permits, we will also study gauged topological sigma models.