Thermal Ground State in Yang-Mills Thermodynamics

TL;DR

This paper derives a priori estimates for the thermal ground state in SU(2) Yang-Mills thermodynamics, revealing how nonperturbative effects and monopole-antimonopole pairs influence the effective theory and gauge symmetry breaking.

Contribution

It introduces a selfconsistent coarse-graining approach over calorons to derive the effective ground state and explores its implications for gauge symmetry and thermodynamics.

Findings

The effective action is local and simple due to renormalizability.

The temperature dependence of the coupling describes Coulomb screening.

Monopole-antimonopole pairs arise as small-holonomy excitations.

Abstract

We derive an a useful priori estimate for the thermal ground state of deconfining phase of SU(2) Yang-Mills thermodynamics in four-dimensional, flat spacetime and discuss its implications. Upon a selfconsistent spatial coarse-graining over noninteracting, trivial-holonomy (BPS saturated) (anti)calorons of unit topological charge modulus an inert, adjoint scalar field $|\phi|$ and an effective pure-gauge configuration $a_\mu^{gs}$ emerge. The modulus $|\phi|>0$ defines the maximal resolution in the coarse-grained theory and induces dynamical gauge-symmetry breaking. Thanks to perturbative renormalizability and the fact that |phi| can not absorb or emit energy-momentum the effective action is local and simple. The temperature dependence of the effective coupling is a consequence of thermodynamical consistency and describes the Coulomb screening of a static test charge due to short-lived monopole-antimonopole pairs. The latter occur unresolvably as small-holonomy excitations of (anti)calorons by the absorption of propagating fundamental gauge fields.