Non-Perturbative Groundstate of High Temperature Yang-Mills Theory

TL;DR

This paper challenges the validity of the perturbative groundstate in high-temperature Yang-Mills theory, showing that non-perturbative effects dominate and lattice simulations reveal nonzero expectation values of A0, indicating limitations of perturbation theory.

Contribution

It demonstrates that the perturbative effective potential is invalid at high temperatures due to infrared divergences, emphasizing the importance of non-perturbative effects in the thermal groundstate.

Findings

Infrared divergence invalidates the perturbative groundstate.

Lattice simulations show nonzero, non-perturbative A0 expectation values.

Perturbation theory cannot fully describe thermodynamic quantities at high T.

Abstract

The effective potential of Yang-Mills theory at high temperature derived by Gross, Pisarski, Yaffe and Weiss is critically reexamined and it is argued that the groundstate of the potential at <A0>=0 is invalid, due to the infrared divergence of the Matsubara zero mode. This suggests that the thermal groundstate is dominated by infrared non-perturbative effects. Lattice simulations are carried out and the field A0 in the static gauge is observed to acquire nonzero, non-perturbative expectation values at high temperatures. A consequence is that thermal perturbation theory is inconsistent with the non-perturbative groundstate and it cannot account for all of the contributions to a thermodynamic quantity at any temperature. Related issues, including dimensional reduction and confinement, are also discussed.