Infrared phases of 3d massless CS-QCD and large $N_f$

TL;DR

This paper analyzes the anomalous dimensions of quartic operators in 3D massless CS-QCD, revealing potential symmetry-breaking instabilities and connections to 4D QCD phenomena, using large N_f and N_c limits for analytic control.

Contribution

It provides the first detailed analysis of quartic operator anomalous dimensions in 3D CS-QCD with large N_f and N_c, linking 3D and 4D QCD behaviors.

Findings

Operators become marginal, indicating possible symmetry breaking.

Critical N_f* close to the conformal window of 4D QCD.

No symmetry breaking observed in bosonic CS-QCD3 within analysis scope.

Abstract

We compute anomalous dimensions of quartic operators which are singlets under the $\mathrm{U}(N_f)$ global symmetry in Yang-Mills theories with Chern-Simons level $k$ in three dimensions coupled to $N_f$ Dirac fermions. In order to have analytic control, we consider the regime $N_f\gg N_c\gg 1$, where the problem is reduced to the study of a flavor-adjoint and a flavor-singlet bilinears whose square give the quartic operators of interest. We provide evidence that these operators hit marginality, signaling instabilities which, for $\frac{2k}{N_f}<1$ suggest the spontaneous breaking of the global symmetry, and no symmetry breaking otherwise. For $k=N_f/2-1$ (the value corresponding to the domain walls of 4d QCD at $\theta=\pi$), the critical value $N_f^*$ is tantalizingly close to the lower end of the conformal window of QCD$_4$, suggesting a connection between conformal and global symmetry breaking in the 4d theory and in its domain walls. We also study, at $k=0$, other quartic operators containing a singlet when branched under $\mathrm{U}\left(\frac{N_f}{2}\right)\times \mathrm{U}\left(\frac{N_f}{2}\right)$, finding that they hit marginality precisely at the same point as their flavor-neutral cousins. Using the same technology we study bosonic CS-QCD$_3$, finding no hint of symmetry breaking where our analysis is applicable.