Center Symmetry and Abelian Projection at Finite Temperature

TL;DR

This paper demonstrates that Abelian projection at finite temperature preserves the universality class of the original gauge theory, resolving apparent conflicts with critical universality through non-local effective action terms.

Contribution

It proves that the projected theory retains the universality class of the parent gauge theory by analyzing non-local terms involving Polyakov loops.

Findings

Projected theory shares the universality class of the original gauge theory.

Non-local terms in the effective action involving Polyakov loops are crucial.

Connects Abelian projection results to deconfinement transition studies.

Abstract

At finite temperature, there is an apparent conflict between Abelian projection and critical universality. For example, should the deconfinement transition of an SU(2) gauge theory projected to U(1) lie in the Z(2) universality class of the parent SU(2) theory or in the U(1) universality class? I prove that the projected theory lies in the universality class of the parent gauge theory. The mechanism is shown to be non-local terms in the projected effective action involving Polyakov loops. I connect this to the recent work by Dunne et al. on the deconfinement transition in the 2+1 dimensional Georgi-Glashow model.