Discrete $\beta$-function of the SU(3) gauge theory with 10 massless domain-wall fermions
I present the updated results of the discrete $\beta$-function of the $SU(3)$ gauge theory with $N_f=10$ massless optimal domain-wall fermions in the fundamental representation. The renormalized coupling is obtained by the finite-volume gradient flow scheme on $L^4$ lattices, for seven lattice sizes: $L/a=8,10,12,16,20,24,32$; and each with $12$ different lattice spacings parametrized by $6/g^2$. The discrete $\beta$-function is extrapolated to the continuum limit using four lattice pairs $(L,2L)/a=(8,16),(10,20),(12,24) $ and $ (16,32) $. This provides stronger evidence of the infrared fixed point at $g_c^2 \sim 7$, which was first reported in arXiv:1603.08854, based on the continuum extrapolation of the discrete $\beta$-function obtained with three lattice pairs.