Two-dimensional N = (0, 4) supersymmetric quiver gauge theories are realized as D3-brane box configurations (two dimensional intervals) which are bounded by NS5-branes and intersect with D5-branes. The periodic brane configuration is mapped to D1-D5-D5 brane system at orbifold singularity via T-duality. The matter content and interactions are encoded by the N = (0, 4) quiver diagrams which are determined by the brane configurations. The Abelian gauge anomaly cancellation indicates the presence of Fermi multiplets at the NS-NS junction. We also discuss the brane construction of N = (0, 4) supersymmetric boundary conditions in 3d N = 4 gauge theories involving two-dimensional boundary degrees of freedom that cancel gauge anomaly.

We propose a universal IR formula for the protected three-sphere correlation functions of Higgs and Coulomb branch operators of N = 4 supersymmetric quantum field theories with massive, topologically trivial vacua.7 Also see [4][5][6].

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.

We compute supersymmetric indices which count local operators at certain half-BPS interfaces and quarter-BPS junctions of interfaces in four-dimensional $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We use the indices as very stringent tests of a variety of string theory-inspired conjectures about the action of S-duality on such defects.

We study supersymmetric boundary conditions in three-dimensional N ¼ 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 ¼ 2 Maxwell theory with boundary and the Abelian duality. Finally we make some comments on N ¼ 2 SQED with boundary condition and the mirror symmetry.1 Here we use the term ''membrane'' in a broad meaning. We do not claim that our membrane is the same as that considered in M theory.