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

Abstract

We study three-dimensional 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 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.

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

“…In general, the Coulomb branch is drastically modified and different from the classical picture. In [5], we studied the 3d N = 2 Spin(7) gauge theory with vector and spinor matters. We found that the Coulomb moduli space is one-or two-dimensional depending on the matter contents and also found various s-confinement phases.…”

“…These were studied in [8,9] for the cases where the theory contains JHEP03(2019)113 only vector matters. In [5], we studied these operators in the 3d N = 2 Spin(7) theory with vector and spinor matters. In these examples, we found that almost all the classical Coulomb branches are lifted and the quantum Coulomb moduli space is described by only a few operators.…”

“…n−1 Y n can survive the non-perturbative effects and become exactly massless. The second Coulomb branch denoted as Z appears when the Spin(N ) theory includes spinor matters or when we put the 4d N = 1 Spin(N ) theory on a circle [5,[8][9][10][11]. This operator corresponds to the gauge symmetry breaking…”

“…. In order to make the vacuum of the low-energy SO(7) theory stable, we have to take (N v , N s ) above the s-confinement bound of the Spin 7theory, which was studied in [5].…”

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

“…These were studied in [8,9] for the cases where the theory contains only the vector matters. In [5], we studied these operators in the Spin (7) theory with vector and spinor matters. In these examples, we learned that almost all the classical Coulomb branches are lifted and the quantum Coulomb moduli space is described by only a few operators.…”