Thermal effective potential for the Polyakov loop to higher loop order

Abstract

This is a progress report on the calculation of the effective potential for the Polyakov loop in $SU(N)$ pure gauge theory beyond two-loop order. We introduce a new approach using the Poisson resummation formula to compute sum-integrals with the holonomy. We show partial results for the free energy at order $g^3$ and $g^4$.