Confinement at Weak Coupling

TL;DR

This paper explores the perturbative stability of center-symmetric configurations in weakly coupled gauge theories, investigates a constrained SU(2) lattice model, and discusses the finite temperature phase transition and transfer matrix construction.

Contribution

It extends previous work by analyzing models with stable perturbative expansions and provides a framework for understanding phase transitions in constrained gauge theories.

Findings

Perturbative expansion remains stable in extended models.

Finite temperature phase transition observed in constrained SU(2) lattice gauge theory.

Transfer matrix constructed for constrained SU(N) gauge theories at finite temperature.

Abstract

The free energy of U(N) and SU(N) gauge theory was recently found to be of order N^0 to all orders of a perturbative expansion about a center-symmetric orbit of vanishing curvature. Here I consider extended models for which this expansion is perturbatively stable. The extreme case of an SU(2) gauge theory whose configuration space is restricted to center-symmetric orbits has recently been investigated on the lattice hep-lat/0509156. In extension of my talk, a discussion and possible interpretation of the observed finite temperature phase transition is given. The transfer matrix of constrained SU(N) lattice gauge theory is constructed for any finite temperature.