On the absence of a deconfining phase transition for the savvidy model at one-loop order

Abstract

The finite-temperature QCD effective action for a constant, chromomagnetic background field, at one-loop order, is shown to undergo a transition from the confining to a non-confining phase, for sufficiently high temperature only if unstable modes are suppressed, but not if they are taken into account. This result remains the same when massless or massive quarks are present. The proof is made using a quantum field theoretical description of the finite-temperature effects, and zeta-function regularization. The real and imaginary contributions of the unstable modes are calculated in detail. It turns out that, at high temperature, the imaginary part is a term of leading order inT, so that the instabilities of the vacuum never disappear and are responsible for the absence of symmetry restauration in this model, even if quarks are present.