3d exceptional gauge theories and boundary confinement

Abstract

We find boundary confining dualities of 3d $\mathcal{N}$ = 2 supersymmetric gauge theories with exceptional gauge groups. The half-indices which enumerate the boundary BPS local operators in the presence of Neumann and Dirichlet boundary conditions for gauge fields are identified with the Askey-Wilson type q-beta integrals and Macdonald type sums respectively. New conjectural identities of E₆ and E₇ integrals and sums are derived from the boundary confining dualities. We also consider theories with a vector multiplet and adjoint chiral, which correspond to an $\mathcal{N}$ = 4 vector multiplet, with appropriate boundary conditions. We argue for the boundary confinement of the $\mathcal{N}$ = 4 vector multiplet and comment on such theories also with classical gauge groups.