Supersymmetric Boundary Conditions in Three Dimensional N = 2 Theories

TL;DR

This paper classifies supersymmetric boundary conditions in 3D N=2 theories, identifying geometric conditions for A-type and B-type branes in Landau-Ginzburg models and exploring dualities and mirror symmetry implications.

Contribution

It provides a systematic classification of boundary conditions preserving supersymmetry in 3D N=2 theories, linking them to geometric submanifolds and duality transformations.

Findings

A-type branes are Lagrangian submanifolds with constant imaginary superpotential

B-type branes are holomorphic submanifolds with constant superpotential

Discussion of boundary conditions in Maxwell theory and mirror symmetry insights

Abstract

We study supersymmetric boundary conditions in 3-dimensional N = 2 Landau-Ginzburg models and abelian gauge theories. In the Landau-Ginzburg model the boundary conditions that preserve (1,1) supersymmetry (A-type) and (2,0) supersymmetry (B-type) on the boundary are classified in terms of subspaces of the target space ("brane"). An A-type brane is a Lagrangian submanifold on which the imaginary part of the superpotential is constant, while a B-type brane is a holomorphic submanifold on which the superpotential is constant. We also consider the N = 2 Maxwell theory with boundary and the abelian duality. Finally we make some comments on N = 2 SQED with boundary condition and the mirror symmetry.