Topological susceptibility of SU(N) gauge theories at finite temperature

TL;DR

This study examines how the topological susceptibility in SU(N) gauge theories behaves at finite temperature, revealing it remains stable below the transition but diminishes above, with implications for large-N limits.

Contribution

It provides the first lattice Monte Carlo analysis of the large-N behavior of topological susceptibility across the finite-temperature transition in SU(N) gauge theories.

Findings

Topological susceptibility remains nonzero below Tc at large N.

Above Tc, the susceptibility is significantly suppressed.

Data suggests a vanishing large-N limit for T>Tc.

Abstract

We investigate the large-N behavior of the topological susceptibility in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at Tc. For this purpose, we consider the lattice formulation of the SU(N) gauge theories and perform Monte Carlo simulations for N=4,6. The results indicate that the topological susceptibility has a nonvanishing large-N limit for T<Tc, as at T=0, and that the topological properties remain substantially unchanged in the low-temperature phase. On the other hand, above the deconfinement phase transition, the topological susceptibility shows a large suppression. The comparison between the data for N=4 and N=6 hints at a vanishing large-N limit for T>Tc.