Conundrum for the free energy of a holonomous gluonic plasma at cubic order
Résumé
We compute the term ∼g3 in the free energy for a SU(N) gauge theory with nonzero holonomy at nonzero temperature. If the holonomy is generated kinematically by the introduction of gauge invariant sources coupled to Polyakov loops, the contribution of charged (off-diagonal) gluons to the free energy at order g3 , F(3:c.g.) , is singular: F(3:c.g.)≠0 without holonomy, but F(3:c.g.)=0 when the holonomy is nonzero, even infinitesimally. We show that the absence of the charged gluon contribution is required by gauge invariance alone and is therefore a universal feature.