Spontaneous magnetization of a vacuum in high temperature gluodynamics (two-loop approximation

TL;DR

This paper calculates the two-loop effective potential in high-temperature SU(N) gluodynamics to analyze the simultaneous spontaneous generation of chromomagnetic and A_0 condensates, showing A_0 stabilizes the magnetized vacuum.

Contribution

It extends previous work by computing the two-loop effective potential for both condensates and demonstrating how A_0 stabilizes the magnetic vacuum at high temperature.

Findings

A_0 condensate stabilizes the chromomagnetic vacuum.

The two-loop effective potential confirms simultaneous condensate generation.

Results agree with lattice simulations.

Abstract

In SU(N) gluodynamics, at high temperature the spontaneous magnetization, b(T) not equal to 0, of a vacuum happens in the approximation to the effective potential - the tree plus the one-loop, plus daisy diagrams, W(b)= b^2/2 g^2 + W^(1)(b) + W^(daisy)(b). At the same time, in two-loop approximation, W(A_0)= W^(1)(A_0) + W^(2)(A_0), other classical field - A_0 condensate directly related to the Polyakov loop - is also spontaneously generated. To investigate the creation of the condensates together, the two loop effective potential of both fields should be calculated. This program was realized recently for SU(2) in [1]. However, the generation of magnetic field in two-loop order was not studied in detail. In the present paper, we compute the value of chromomagnetic field b(T) for latter case. Then, considering the spectrum of color charged gluons at the background of both condensates, we conclude that the A_0 stabilizes the magnetized vacuum at high temperature. This is in agreement with the lattice simulations carried out already and clarifies the mechanism of the magnetic field stabilization. Key words: condetsation, high temperature, gluodynamics, A0 condensate, spontaneous magnetization, vacuum