Covariant variational approach to Yang-Mills Theory: effective potential of the Polyakov loop

TL;DR

This paper develops a covariant variational method to compute the effective potential of the Polyakov loop in SU(2) and SU(3) Yang-Mills theories, revealing phase transition signals consistent with lattice results.

Contribution

It extends the covariant variational approach to background gauge and relates Green's functions to Landau gauge results, providing a new way to study deconfinement transitions.

Findings

Identifies second order deconfinement transition for SU(2).

Finds first order transition for SU(3).

Critical temperatures align with lattice data.

Abstract

We compute the effective action of the Polyakov loop in SU(2) and SU(3) Yang-Mills theory using a previously developed covariant variational approach. The formalism is extended to background gauge and it is shown how to relate the low order Green's functions to the ones in Landau gauge studied earlier. The renormalization procedure is discussed. The self-consistent effective action is derived and evaluated using the numerical solution of the gap equation. We find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for SU(2) and first order for SU(3). The critical temperatures obtained are in reasonable agreement with high precision lattice data.