$A_0$ condensation, Nielsen's identity and effective potential of order parameter

TL;DR

This paper investigates A_0 condensation in high-temperature SU(2) gluodynamics, demonstrating gauge invariance of the phenomenon through effective potential analysis and establishing a link with the Polyakov loop as an order parameter.

Contribution

It recalculates the two-loop effective potential in a relativistic R_xi gauge, showing gauge invariance and deriving a gauge-independent effective potential related to the Polyakov loop.

Findings

Effective potential has a nontrivial minimum indicating A_0 condensation.

The potential is xi-independent and matches the gauge-invariant description.

The minimum Polyakov loop value is computed and compared with other studies.

Abstract

In high temperature SU(2) gluodynamics, the condensation of the zero component gauge field potential A_0 =const and its gauge-fixing dependence are investigated. A_0 is mutually related with Polyakov's loop <L>. The two-loop effective potential W(A_0,xi) is recalculated in the background relativistic R_xi gauge. It depends on the parameter xi, has a nontrivial minimum and satisfies Nielsen's identity. These signs mean gauge invariance of the condensation phenomenon. Following the idea of Belyaev, we express W(A_0,xi) in terms of <L>. The obtained effective potential of order parameter differs from that derived by this author. It is independent of xi and has a nontrivial minimum position. Hence the A_0 condensation follows. We show that the equation relating A_0 and (A_0)|_(classical) coincides with the special characteristic orbit in the (A)$-plain along which the W(A_0,xi) is xi-independent. In this way the link between these two gauge invariant descriptions is established. The minimum value of the Polyakov loop is calculated. Comparison with results of other authors is given.