Perturbative evaluation of the thermal Wilson loop

Abstract The thermal Wilson loop × tr P exp [ i g ∫ β 0 d τ A 0 (τ, x)]> , representing an order parameter for the gauge theory and expected to be zero in the confining phase, is perturbatively evaluated up to the O( g 4 ) included for an SU( N ) pure Yang-Mills theory. This evaluation should be meningful at high temperature, β→0. Its behaviour is discussed and a possible need for non-perturbative instanton-like contributions is pointed out.