Change of theta dependence in 4D SU(N) gauge theories across the deconfinement transition

TL;DR

This study examines how the dependence of 4D SU(N) gauge theories on the topological theta term changes across the deconfinement transition, revealing a shift from large-N scaling to instanton-gas behavior at high temperatures.

Contribution

It provides numerical evidence of a sharp change in theta dependence across the deconfinement transition, highlighting different scaling regimes at low and high temperatures for SU(N) gauge theories.

Findings

Theta dependence shifts from theta/N scaling to theta scaling across Tc.

The transition becomes sharper with increasing N.

Instanton-gas approximation describes high-temperature phase.

Abstract

We investigate the dependence of four-dimensional SU(N) gauge theories on the topological theta term at finite temperature and, in particular, across the deconfinement transition. For this purpose, we exploit the lattice formulation of the theory and present numerical results for the expansion of the free energy up to O(theta^6), for N=3 and N=6. Our numerical analysis shows that the theta dependence of 4D SU(N) gauge theory experiences a drastic change across the deconfinement transition: the low-temperature phase is characterized by a large-N scaling with theta/N as relevant variable, while in the high-temperature phase the scaling variable is just theta and the free energy is essentially determined by the instanton-gas approximation. The crossover between the two different behaviours gets sharper with increasing N, suggesting that the instanton-gas regime sets in just above Tc at large N.