Z(N) interface tension in a hot SU(N) gauge theory

TL;DR

This work analyzes the Z(N) interface tension in hot SU(N) gauge theory without fermions and computes it to next-to-leading order in weak coupling. It introduces a constrained, one-dimensional effective-action framework to reduce the four-dimensional gauge theory to a Z(N) instanton problem in an effective theory, employing zeta-function techniques for loop integrals. The leading result yields $\alpha_{LO} = \frac{4 (N-1) \pi^2}{3 \sqrt{3N}} \frac{T^3}{g}$, while the next-to-leading correction with running coupling $g(T)$ gives $\alpha_{NLO} = \alpha_{LO} \left( 1 - (15.2785...) \frac{g^2(T) N}{16 \pi^2} \right)$. The authors show gauge-independence for zero-energy instantons and argue that charge conjugation symmetry is preserved up to two loops, conjecturing this holds to all orders, with implications for the high-temperature phase structure of non-Abelian gauge theories.

Abstract

The interface tension between Z(N) vacua in a hot SU(N) gauge theory (without dynamical fermions) is computed at next to leading order in weak coupling. The Z(N) interface tension is related to the instanton of an effective action, which includes both classical and quantum terms; a general technique for treating consistently the saddle points of such effective actions is developed. Loop integrals which arise in the calculation are evaluated by means of zeta function techniques. As a byproduct, up to two loop order we find that the stable vacuum is always equivalent to the trivial one, and so respects charge conjugation symmetry.