A Symmetry Breaking Scenario for QCD$_3$

TL;DR

This paper proposes a novel symmetry breaking scenario in 2+1 dimensional $SU(N)$ gauge theories with Chern-Simons terms, revealing a range of flavor numbers where spontaneous symmetry breaking occurs with nontrivial Goldstone dynamics.

Contribution

It introduces a new symmetry breaking mechanism in 2+1D gauge theories with Chern-Simons terms, including the role of Wess-Zumino terms and dual scalar theories, extending understanding beyond 3+1D cases.

Findings

Symmetry breaks for $N_f > 2k$ in a range of quark masses.

Goldstone bosons require Wess-Zumino terms for consistency.

Proposes dual scalar theories for the symmetry breaking regime.

Abstract

We consider the dynamics of 2+1 dimensional $SU(N)$ gauge theory with Chern-Simons level $k$ and $N_f$ fundamental fermions. By requiring consistency with previously suggested dualities for $N_f\leq 2k$ as well as the dynamics at $k=0$ we propose that the theory with $N_f> 2k$ breaks the $U(N_f)$ global symmetry spontaneously to $U(N_f/2+k)\times U(N_f/2-k)$. In contrast to the 3+1 dimensional case, the symmetry breaking takes place in a range of quark masses and not just at one point. The target space never becomes parametrically large and the Nambu-Goldstone bosons are therefore not visible semi-classically. Such symmetry breaking is argued to take place in some intermediate range of the number of flavors, $2k< N_f< N_*(N,k)$, with the upper limit $N_*$ obeying various constraints. The Lagrangian for the Nambu-Goldstone bosons has to be supplemented by nontrivial Wess-Zumino terms that are necessary for the consistency of the picture, even at $k=0$. Furthermore, we suggest two scalar dual theories in this range of $N_f$. A similar picture is developed for $SO(N)$ and $Sp(N)$ gauge theories. It sheds new light on monopole condensation and confinement in the $SO(N)$ and $Spin(N)$ theories.