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

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.

arXiv comment10 pages

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