Color dependence of the topological susceptibility in Yang-Mills theories

Abstract

For Yang-Mills theories in four dimensions, we propose to rescale the ratio between topological susceptibility and string tension squared in a universal way, dependent only on group factors. We apply this suggestion to SU (Nc) and Sp(Nc) groups, and compare lattice measurements performed by several independent collaborations. We show that the two sequences of (rescaled) numerical results in these two families of groups are compatible with each other. We hence perform a combined fit, and extrapolate to the common large-Nc limit.

Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks

“…Numerical simulations of the pure gauge theory find that the dependence on N is rather weak. Forming a dimensionless ratio between the topological susceptibility and the square of the string tension, at zero temperature χ top (0)/σ 2 , only varies by ≈ 10% between N = 3 [31][32][33][34][35][36] and higher N [37][38][39][40][41][42][43][44][45][46][47][48][49][50]. These results suggest that as N → ∞, the topological susceptibility does not vary with temperature in the confined phase.…”