Renormalization - Group Study of Four - Dimensional Su ( 4 ) Gauge Theory

In some recent papers, we studied pure SU(4) gauge theory with the Wilson action on a hypercubical lattice in four space t ime dimensions and found a firstorder phase transition at/3 = 10.2 [1 ], that this phase transition was not deconfining [2] and measured the asymptotic freedom scale parameter A 0 [2]. In the present paper, we wish to apply a renormalizationgroup scheme [3] for comparing the bare coupling constants at different cutoff values, to the gauge group SU(4). This procedure was previously successfully applied to SU(2) [3] and SU(3) [4]. In order to implement this renormalization-group procedure to SU(4), we measure all Wilson loops up to size 4 X 4 on an 8 4 lattice. Although the gauge group of interest to the strong interactions is SU(3), there are interesting reasons to extend these renormalization group studies to SU(4). First, considerable work has gone into using the in-