Hot gluon matter in a constantA 0 background

Abstract

We compute the effective action of finiteT SU(3) gauge theory in a constant diagonal background fieldA 0(t,x)=B 0 3 T3+B 0 8 T8 in the general covariant background gauge up to terms of orderg 3.B 0 3,8 shield the infrared singularities and the aim is to study whether the minimum of the effective action would determine their values dynamically. We find that the orderg 2 term depends explicitly on the gauge fixing parameter ξ. Since the background field screens already at the tree diagram level the interactions of the six non-diagonal gluon fields they do not contribute to the plasmon-likeg 3 term. The two diagonal fieldsA 0 3 ,A 0 8 do, but the electric mass squared they develop will become negative if the background fields are larger than aboutT/g. Hence large background fields make the system unstable.