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QCD with gauge group $SU(N_c)$ flows to an interacting conformal fixed pointin 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 offermions is lowered to $N_f^{\rm crit} \approx {11 \over 2} N_c + (6 + {4 \overN_c}) \epsilon$, a certain four-fermion operator becomes relevant and thetheory flows to a new infrared fixed point (massless or massive). F-theorem orentanglement monotonicity considerations complement our $\epsilon$-expansioncalculation.

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