N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models

TL;DR

This paper classifies and analyzes N=2 superconformal boundary conditions for two-dimensional sigma models and Landau-Ginzburg models, revealing new geometric structures and boundary conditions on Kahler and bihermitian target spaces.

Contribution

It systematically determines the most general local N=2 superconformal boundary conditions for these models, including new results on coisotropic A-branes and boundary conditions on bihermitian manifolds.

Findings

Reproduces known boundary conditions for Kahler models

Identifies new boundary conditions for bihermitian target spaces

Provides geometric interpretation of boundary conditions in terms of submanifolds

Abstract

We study N=2 nonlinear two dimensional sigma models with boundaries and their massive generalizations (the Landau-Ginzburg models). These models are defined over either Kahler or bihermitian target space manifolds. We determine the most general local N=2 superconformal boundary conditions (D-branes) for these sigma models. In the Kahler case we reproduce the known results in a systematic fashion including interesting results concerning the coisotropic A-type branes. We further analyse the N=2 superconformal boundary conditions for sigma models defined over a bihermitian manifold with torsion. We interpret the boundary conditions in terms of different types of submanifolds of the target space. We point out how the open sigma models correspond to new types of target space geometry. For the massive Landau-Ginzburg models (both Kahler and bihermitian) we discuss an important class of supersymmetric boundary conditions which admits a nice geometrical interpretation.