Renormalization Group Flow of SU(3) Gauge Theory

Abstract

We calculate numerically the renormalization group (RG) flow of lattice QCD in two-coupling space, $(β_{1\times 1},β_{1\times 2})$. This is the first explicit calculation of the RG flow of SU(3) gauge theory. From the RG flow,a renormalized trajectory (RT) is revealed. Its behavior is consistent with the strong coupling expansion near the high-temperature fixed point. Actions with $(β_{1\times 1},β_{1\times 2})$ are studied; the lattice spacing is evaluated by measuring the string tension from the heavy quark potential. Recovery of the rotational symmetry is studied as a function of the ratio $β_{1\times 2} / β_{1\times 1}$.