The Finite Temperature SU(2) Savvidy Model with a Non-trivial Polyakov Loop

Abstract

We calculate the complete one-loop effective potential for SU(2) gauge bosons at temperature T as a function of two variables: phi, the angle associated with a non-trivial Polyakov loop, and H, a constant background chromomagnetic field. Using techniques broadly applicable to finite temperature field theories, we develop both low and high temperature expansions. At low temperatures, the real part of the effective potential V_R indicates a rich phase structure, with a discontinuous alternation between confined (phi=pi) and deconfined phases (phi=0). The background field H moves slowly upward from its zero-temperature value as T increases, in such a way that sqrt(gH)/(pi T) is approximately an integer. Beyond a certain temperature on the order of sqrt(gH), the deconfined phase is always preferred. At high temperatures, where asymptotic freedom applies, the deconfined phase phi=0 is always preferred, and sqrt(gH) is of order g^2(T)T. The imaginary part of the effective potential is non-zero at the global minimum of V_R for all temperatures. A non-perturbative magnetic screening mass of the form M_m = cg^2(T)T with a sufficiently large coefficient c removes this instability at high temperature, leading to a stable high-temperature phase with phi=0 and H=0, characteristic of a weakly-interacting gas of gauge particles. The value of M_m obtained is comparable with lattice estimates.