Center-Symmetric Effective Theory for High-Temperature SU(2) Yang-Mills Theory

TL;DR

This paper develops a center-symmetric effective theory for high-temperature SU(2) Yang-Mills, demonstrating that incorporating center symmetry accurately captures the confinement transition through both perturbative and non-perturbative methods.

Contribution

It introduces a novel center-symmetric effective theory that extends the validity of dimensional reduction to the confinement transition in SU(2) Yang-Mills.

Findings

The effective theory reproduces the second order confining phase transition.

Perturbative matching aligns the effective theory with the full theory at high temperatures.

Lattice simulations confirm the phase structure predicted by the effective theory.

Abstract

We construct and study a dimensionally reduced effective theory for high-temperature SU(2) Yang-Mills theory that respects all the symmetries of the underlying theory. Our main motivation is to study, whether the correct treatment of the center symmetry can help extend the applicability of the dimensional reduction procedure towards the confinement transition. After performing perturbative matching to the full theory at asymptotically high temperatures, we map the phase diagram of the effective theory using non-perturbative lattice simulations. We find that at lower temperature the theory undergoes a second order confining phase transition, in complete analogy with the full theory, which is a direct consequence of having incorporated the center symmetry.