Abelian dualities of N $$ \mathcal{N} $$ = (0, 4) boundary conditions

Abstract

Abstract We propose dual pairs of N $$ \mathcal{N} $$ = (0, 4) half-BPS boundary conditions for 3d N $$ \mathcal{N} $$ = 4 Abelian gauge theories related to mirror symmetry and S-duality by showing the matching of boundary ’t Hooft anomalies and supersymmetric indices. We find simple N $$ \mathcal{N} $$ = (0, 4) mirror symmetry between 2d N $$ \mathcal{N} $$ = (0, 4) Abelian gauge theories and free Fermi multiplets that generalizes N $$ \mathcal{N} $$ = (0, 2) Abelian duality. We also propose a prescription for computing half-index of enriched Neumann boundary condition including 2d boundary bosonic matters by gauging the 2d boundary flavor symmetry of Dirichlet boundary condition. By coupling N $$ \mathcal{N} $$ = (0,4) half-BPS boundary configurations of 3d N $$ \mathcal{N} $$ = 4 gauge theories to quarter-BPS corner configurations of 4d N $$ \mathcal{N} $$ = 4 Super Yang-Mills theories, we further obtain a new type of 4d-3d-2d duality that may involve 3d non-Abelian gauge symmetry.

Keywords

• Brane Dynamics in Gauge Theories
• Duality in Gauge Field Theories
• Supersymmetric Gauge Theory
• Supersymmetry and Duality