A Center-Symmetric 1/N Expansion

TL;DR

This paper develops a 1/N expansion of SU(N) gauge theory around a center-symmetric background, revealing a different free energy scaling and infrared behavior compared to traditional approaches, with implications for understanding non-Abelian gauge theories.

Contribution

It introduces a novel center-symmetric background for SU(N) lattice gauge theory and analyzes the resulting 1/N expansion, highlighting differences from spontaneous symmetry breaking scenarios.

Findings

Leading free energy is O(1) instead of O(N^2)

Infrared divergences are absent in the center-symmetric expansion

The 't Hooft coupling decreases as 1/ln(N) for large N

Abstract

The free energy of U(N) gauge theory is expanded about a center-symmetric topological background configuration with vanishing action and vanishing Polyakov loops. We construct this background for SU(N) lattice gauge theory and show that it uniquely describes center-symmetric minimal action orbits in the limit of infinite lattice volume. The leading contribution to the free energy in the 1/N expansion about this background is of O(N^0) rather than O(N^2) as one finds when the center symmetry is spontaneously broken. The contribution of planar 't Hooft diagrams to the free energy is O(1/N^2) and sub-leading in this case. The change in behavior of the diagrammatic expansion is traced to Linde's observation that the usual perturbation series of non-Abelian gauge theories suffers from severe infrared divergences. This infrared problem does not arise in a center-symmetric expansion. The 't Hooft coupling \lambda=g^2 N is found to decrease proportional to 1/\ln(N) for large N. There is evidence of a vector-ghost in the planar truncation of the model.