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

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 $N_f^{\mathrm{crit}}\approx \frac{11}{2}{N}_c+(6+\frac{4}{N_c})\epsilon$, 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.

21 pages, including two appendices and three figures

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