(0,4) brane box models

Two-dimensional N = (0; 4) supersymmetric quiver gauge theories are realized as D3-brane box con fi gurations (two dimensional intervals) which are bounded by NS5-branes and intersect with D5-branes. The periodic brane con fi guration is mapped to D1-D5-D5 0 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 con fi gurations. The Abelian gauge anomaly cancellation indicates the presence of Fermi multiplets at the NS-NS 0 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.