Effective potential for the order parameter of the SU(2) Yang-Mills deconfinement transition

TL;DR

This paper derives an effective potential for the Polyakov loop in SU(2) Yang-Mills theory, capturing the second-order deconfinement transition by integrating out vector fields in a one-loop approximation.

Contribution

It introduces a second-order derivative expansion of the effective potential for the Polyakov loop, providing a new analytical tool to study the deconfinement transition.

Findings

Effective potential describes second-order transition

Analytical form captures temperature dependence

Validates Polyakov loop as order parameter

Abstract

The Polyakov loop variable serves as an order parameter to characterize the confined and deconfined phases of Yang-Mills theory. By integrating out the vector fields in the SU(2) Yang-Mills partition function in one-loop approximation, an effective action is obtained for the Polyakov loop to second order in a derivative expansion. The resulting effective potential for the Polyakov loop is capable of describing a second-order deconfinement transition as a function of temperature.