Improved study of the β-function of SU(3) gauge theory with Nf=10 massless domain-wall fermions,

Ting-Wai Chiu 2019 Physical Review D 99 014507 (2019)

We perform an improved study of the β function of SU(3) lattice gauge theory with Nf=10 massless optimal domain-wall fermions in the fundamental representation, which serves as a check to what extent the scenario we presented previously [Proc. Sci., LATTICE2016 (2017) 228] is valid. In the finite-volume gradient flow scheme with c=8t/L=0.3, the renormalized couplings g^2(L,a) of four primary lattices (L/a={8,10,12,16}) are tuned (in 6/g02) to the same gc2 with statistical error less than 0.5%, in contrast to the previous work where g^2(L,a) were obtained by the cubic-spline interpolation. Then, the renormalized couplings g2(sL,a) of the scaled lattices (sL/a={16,20,24,32} with s=2) are computed at the same 6/g_0^2 of the corresponding primary lattices. Using the renormalized couplings of four lattice pairs (sL,L)/a={(16,8),(20,10),(24,12),(32,16)}, the step-scaling β function [g^2(sL,a)-g^2(L,a)]/ln(s2) is computed and extrapolated to the continuum limit β(s,g_c^2), as summarized in Table III. Based on the four data points of β(s,g_c^2) at g_c^2={6.86(2),6.92(3),7.03(2),7.16(2)}, we infer that the theory is infrared near-conformal, or conformal with the fixed point g*2=7.55(36). This corrects the scenario in the previous work with g*2∼7.0, and also suggests that the interpolation method cannot give a reliable determination of the β function, especially in a regime close to the infrared fixed point.