The $\beta$-function of $SU(3)$ gauge theory with $N_f=10$ massless fermions in the fundamental representation

Abstract

We present the first study of the discrete $\beta$-function of the $SU(3)$ gauge theory with 10 massless domain-wall fermions in the fundamental representation. The renormalized coupling is obtained by the finite-volume gradient flow scheme, and the discrete $\beta$-function is extrapolated to the continuum limit by the step-scaling method. Our result of the discrete $\beta$-function (with $s=2$) suggests that this theory possesses an infrared fixed point around $g_c^2\sim 7.0$ for $c=\sqrt{8t}/L=0.3$.

Comments: 12 pages, 3 eps figures