Effective action for the order parameter of the deconfinement transition of Yang-Mills theories

TL;DR

This paper derives an effective action for the Polyakov loop as an order parameter in Yang-Mills theories, revealing conditions for deconfinement transitions and the impact of infrared effects.

Contribution

It provides a one-loop derivative expansion of the effective action for the Polyakov loop in higher dimensions, highlighting the role of infrared scales in deconfinement.

Findings

Deconfinement transition occurs only for dimensions greater than approximately 7.42.

Infrared effects, such as an effective gluon mass, can induce deconfinement in four dimensions.

The effective action's applicability depends on the dimensionality and infrared dynamics.

Abstract

The effective action for the Polyakov loop serving as an order parameter for deconfinement is obtained in one-loop approximation to second order in a derivative expansion. The calculation is performed in $d\geq 4$ dimensions, mostly referring to the gauge group SU(2). The resulting effective action is only capable of describing a deconfinement phase transition for $d>d_{\text{cr}}\simeq 7.42$. Since, particularly in $d=4$, the system is strongly governed by infrared effects, it is demonstrated that an additional infrared scale such as an effective gluon mass can change the physical properties of the system drastically, leading to a model with a deconfinement phase transition.