(0,4) brane box models

Abstract

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