Abstract
Two-dimensional mathcal{N}=left(0, 4right) 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 mathcal{N}=left(0, 4right) 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 mathcal{N}=left(0, 4right) supersymmetric boundary conditions in 3d mathcal{N}=4 gauge theories involving two-dimensional boundary degrees of freedom that cancel gauge anomaly.
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