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

TL;DR

The paper develops a comprehensive framework for local N=2 boundary conditions on (2,2) supersymmetric sigma models and their Landau–Ginzburg massive generalizations, covering both Kähler and bihermitian target spaces. By combining algebraic, current, and action-based analyses, it derives the most general gluing conditions for B‑type and A‑type branes, including coisotropic A‑branes with B‑field in the Kähler case and intricate bihermitian boundary structures with torsion. It provides geometric interpretations in terms of submanifolds, integrability, and f‑structures, and extends the discussion to boundary potentials in LG models, revealing how holomorphic prepotentials control boundary data. The results illuminate how open sigma models may realize novel target-space geometries and lay groundwork for semiclassical brane constructions in Calabi–Yau and generalized geometric settings. Overall, the work offers a unified, systematic treatment of N=2 boundary conditions across sigma models and LG theories, with clear implications for D-branes in complex and generalized geometries.

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.