Exact results in 3d $$ \mathcal{N} $$ = 2 Spin(7) gauge theories with vector and spinor matters

Abstract

Abstract We study three-dimensional $$ \mathcal{N} $$ N = 2 Spin(7) gauge theories with N S spinorial matters and with N f vectorial matters. The quantum Coulomb branch on the moduli space of vacua is one- or two-dimensional depending on the matter contents. For particular values of (N f , N S ), we find s-confinement phases and derive exact superpotentials. The 3d dynamics of Spin(7) is connected to the 4d dynamics via KK-monopoles. Along the Higgs branch of the Spin(7) theories, we obtain 3d $$ \mathcal{N} $$ N = 2 G 2 or SU(4) theories and some of them lead to new s-confinement phases. As a check of our analysis we compute superconformal indices for these theories.