Low-energy dynamics of 3d N $$ \mathcal{N} $$ = 2 G2 supersymmetric gauge theory

Abstract

We study a three-dimensional N = 2 supersymmetric G 2 gauge theory with and without fundamental matters. We find that a classical Coulomb branch of the moduli space of vacua is partly lifted by monopole-instantons and the quantum Coulomb moduli space would be described by a complex one-dimensional space. Depending on the number of the matters in a fundamental representation, the low-energy dynamics of the theory shows various phases like s-confinement or quantum merging of the Coulomb and the Higgs branches. We also investigate superconformal indices as an independent check of our analysis.

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

“…This superpotential was first obtained in [18]. The similar argument can be applied also for N S ≤ 4 and the G 2 superpotentials are reproduced.…”

“…Along the Higgs branch we find the s-confinement description of the 3d N = 2 G 2 or SU(4) gauge theories with various matters. For the G 2 Higgs branch, we will reproduce the same superpotential discussed in [18]. Along the SU(4) Higgs branch, we reproduce the known s-confinement phases and also find new s-confinement phases for the 3d N = 2 SU(4) gauge theories with anti-symmetric matters.…”

“…which is the superpotential observed in [18]. We can also consider a complex mass deformation for a vectorial matter.…”

“…When a spinor gets a vev M SS,N S N S = v 2 , the theory flows to the 3d N = 2 G 2 gauge theory with N S − 1 fundamentals [18]. The superpotential above correctly explains this flow.…”

“…Next, let us focus on the G 2 direction of the Higgs branch, which is achieved by introducing a vev for a single spinorial field as M SS,44 = v 2 . The low-energy theory becomes a 3d N = 2 G 2 gauge theory with four fundamental matters, which is again sconfining [18]. Although the vev breaks the global SU(4) symmetry to SU(3), we again have the enhanced SU(4) symmetry at the low-energy limit since the vector and the spinors become the same representation in G 2 .…”