Confinement from Correlation Functions

TL;DR

This paper calculates the Polyakov loop potential in Yang--Mills theory using various functional methods, establishing a confinement criterion based on infrared behavior of correlation functions, thereby extending previous work.

Contribution

It introduces a generalized confinement criterion linking infrared correlation functions to the Polyakov loop, applicable across multiple functional approaches.

Findings

Polyakov loop potential computed from dressed correlation functions

Established a confinement criterion based on infrared behavior

Extended previous confinement criteria to general functional methods

Abstract

We compute the Polyakov loop potential in Yang--Mills theory from the fully dressed primitively divergent correlation functions only. This is done in a variety of functional approaches ranging from functional renormalisation group equations over Dyson--Schwinger equations to two-particle irreducible functionals. We present a confinement criterion that links the infrared behaviour of propagators and vertices to the Polyakov loop expectation value. The present work extends the works of [1-3] to general functional methods and sharpens the confinement criterion presented there. The computations are based on the thermal correlation functions in the Landau gauge calculated in [4-6].