Phases Of Adjoint QCD$_3$ And Dualities

TL;DR

This paper explores the phases and dualities of 2+1D adjoint QCD with Chern-Simons terms, revealing quantum phases, supersymmetry breaking, and proposing new dualities and phase diagrams based on symmetry and anomaly considerations.

Contribution

It introduces a quantum phase of adjoint QCD with a TQFT, discusses supersymmetry breaking, and conjectures new fermion-fermion dualities and phase diagrams for various gauge groups.

Findings

Identification of a quantum phase described by a TQFT

Evidence of spontaneous supersymmetry breaking with a Goldstino

Proposal of new dualities and phase diagrams for gauge theories

Abstract

We study 2+1 dimensional gauge theories with a Chern-Simons term and a fermion in the adjoint representation. We apply general considerations of symmetries, anomalies, and renormalization group flows to determine the possible phases of the theory as a function of the gauge group, the Chern-Simons level $k$, and the fermion mass. We propose an inherently quantum mechanical phase of adjoint QCD with small enough $k$, where the infrared is described by a certain Topological Quantum Field Theory (TQFT). For a special choice of the mass, the theory has ${\cal N}=1$ supersymmetry. There this TQFT is accompanied by a massless Majorana fermion - a Goldstino signaling spontaneous supersymmetry breaking. Our analysis leads us to conjecture a number of new infrared fermion-fermion dualities involving $SU$, $SO$, and $Sp$ gauge theories. It also leads us to suggest a phase diagram of $SO/Sp$ gauge theories with a fermion in the traceless symmetric/antisymmetric tensor representation of the gauge group.