Supersymmetric boundary conditions in three-dimensional N=2 theories

We study supersymmetric boundary conditions in three-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.