Conundrum for the free energy of a holonomous gluonic plasma at cubic order

Abstract

We compute the term $\sim g^3$ 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 $g^3$, ${\mathcal{F}}^{\left(3:c.g.\right)}$, is singular: ${\mathcal{F}}^{\left(3:c.g.\right)}\ne 0$ without holonomy, but ${\mathcal{F}}^{\left(3:c.g.\right)}=0$ 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.

Comments: 14 pages