Gauge Fields Condensation at Finite Temperature

TL;DR

This paper recalculates the two-loop effective action for SU(3) gauge theory at finite temperature, examining gauge invariance, vacuum stability, and infrared effects, revealing that higher-order corrections can alter the vacuum state.

Contribution

It provides a gauge-invariant thermodynamical potential calculation at two-loop order and analyzes the stability of the gauge condensate at finite temperature.

Findings

Stable vacuum is trivial at two-loop order.

Higher-order corrections can break the trivial vacuum stability.

Infrared peculiarities are discussed in the context of gauge condensates.

Abstract

The two-loop effective action for the SU(3) gauge model in a constant background field ${\bar A}_0(x,t)=B_0^3T_3+B_0^8T_8$ is recalculated for a gauge with an arbitrary $\xi$-parameter. The gauge-invariant thermodynamical potential is found and its extremum points are investigated. Within a two-loop order we find that the stable nontrivial vacuum is completely equivalent to the trivial one but when the high order corrections being taken into account the indifferent equilibrium seems to be broken. Briefly we also discuss the infrared peculiarities and their status for the gauge models with a nonzero condensate.