Phases of Two Adjoints QCD$_{3}$ And a Duality Chain

TL;DR

This paper explores dualities and phase structures in 2+1D QCD with adjoint fermions, revealing emergent topological phases and symmetry breaking scenarios through a duality chain framework.

Contribution

It introduces new fermion-fermion dualities and a duality chain approach to analyze strongly-coupled phases in adjoint QCD$_{3}$, including symmetry breaking and topological phenomena.

Findings

Identification of strongly coupled quantum phases with topological field theories

Prediction of spontaneous symmetry breaking in specific cases

Application of $SL(2,\

Abstract

We analyze the 2+1 dimensional gauge theory with two fermions in the real adjoint representation with non-zero Chern-Simons level. We propose a new fermion-fermion dualities between strongly-coupled theories and determine the quantum phase using the structure of a `Duality Chain'. We argue that when Chern-Simons level is sufficiently small, the theory in general develops a strongly coupled quantum phase described by an emergent topological field theory. For special cases, our proposal predicts an interesting dynamical scenario with spontaneous breaking of partial 1-form or 0-form global symmetry. It turns out that $SL(2,\mathbb Z)$ transformation and the generalized level/rank duality are crucial for the unitary group case. We further unveil the dynamics of the 2+1 dimensional gauge theory with any pair of adjoint/rank-two fermions or two bifundamental fermions using similar `Duality Chain'.