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

Abstract

We study three-dimensional $\mathcal{N}=2$ $Spin(7)$ 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 $\mathcal{N}=2$ $G_2$ 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.