Dynamics of QCD$_{3}$ with Rank-Two Quarks And Duality

TL;DR

This paper investigates the nonperturbative dynamics of 3D SU(N) gauge theories with rank-two fermions, revealing phase transitions, dualities, and implications for domain walls and anomalies in related gauge theories.

Contribution

It introduces new dualities and phase structures for 3D gauge theories with rank-two fermions, connecting to 4D theories and domain wall physics.

Findings

Emergent topological phases at small Chern-Simons levels

Spontaneous baryon symmetry breaking at zero Chern-Simons level

New fermion-fermion dualities involving two-index representations

Abstract

Three-dimensional gauge theories coupled to fermions can develop interesting nonperturbative dynamics. Here we study in detail the dynamics of $SU(N)$ gauge theories coupled to a Dirac fermion in the rank-two symmetric and antisymmetric representation. We argue that when the Chern-Simons level is sufficiently small the theory develops a quantum phase with an emergent topological field theory. When the Chern-Simons level vanishes, we further argue that a baryon condenses and hence baryon symmetry is spontaneously broken. The infrared theory then consists of a Nambu-Goldstone boson coupled to a topological field theory. Our proposals also lead to new fermion-fermion dualities involving fermions in two-index representations. We make contact between our proposals and some recently discussed aspects of four-dimensional gauge theories. This leads us to a proposal for the domain wall theories of non-supersymmetric gauge theories with fermions in two-index representations. Finally, we discuss some aspects of the time-reversal anomaly in theories with a one-form symmetry.