Stability of $SU(N_c)$ QCD3 from the $\epsilon$-Expansion

TL;DR

This paper investigates the stability of the conformal fixed point in three-dimensional $SU(N_c)$ QCD using the $ ext{epsilon}$-expansion, identifying a critical fermion number where the theory transitions to a different phase.

Contribution

It provides a novel analysis of the fixed point stability in $SU(N_c)$ QCD3 through the $ ext{epsilon}$-expansion, revealing the critical fermion number for phase transition.

Findings

Identification of a critical fermion number $N_f^{ m crit}$ for fixed point stability.

Discovery that a four-fermion operator becomes relevant below $N_f^{ m crit}$.

Complementary use of F-theorem and entanglement monotonicity in analysis.

Abstract

QCD with gauge group $SU(N_c)$ flows to an interacting conformal fixed point in three spacetime dimensions when the number of four-component Dirac fermions $N_f \gg N_c$. We study the stability of this fixed point via the $\epsilon$-expansion about four dimensions. We find that when the number of fermions is lowered to $N_f^{\rm crit} \approx {11 \over 2} N_c + (6 + {4 \over N_c}) \epsilon$, a certain four-fermion operator becomes relevant and the theory flows to a new infrared fixed point (massless or massive). F-theorem or entanglement monotonicity considerations complement our $\epsilon$-expansion calculation.