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.

14 pages

References in corpus (3)

• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• New Phases of SU(3) and SU(4) at Finite Temperature
• How Wide is the Transition to Deconfinement?

Cited by in corpus (8)

• Free energy of a Holonomous Plasma
• Effective models of a semi-quark gluon plasma
• Collisional energy loss of a heavy quark in a semiquark-gluon plasma
• Resummed Gluon Propagator and Debye Screening Effect in a Holonomous Plasma
• Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
• Wilson loops in the Hamiltonian formalism
• Shear and bulk viscosity for a pure glue theory using an effective matrix model
• $A_0$ condensation, Nielsen's identity and effective potential of order parameter