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

Abstract

In SU(N) gluodynamics, at high temperature the spontaneous magnetization, b(T) ≠ 0, of a vac­uum happens in the approximation to the effective potential ­- the tree plus the one-­loop, plus daisy diagrams, W(b) = b2/2g2 + W(1)(b) + W^daisy(b). At the same time, in two­-loop approximation, W(A0) = W(1) (A₀) + W(2)(A₀), other classical field ­ A0 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 A₀ 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.