Abstract
At a nonzero temperature T, a constant field $\overline{A}_0 \sim T/g$ generates nontrivial eigenvalues of the thermal Wilson line. We discuss contributions to the free energy of such a holonomous plasma when the coupling constant, $g$, is weak. We review the computation to $\sim g^2$ by several alternate methods, and show that gauge invariant sources, which are nonlinear in the gauge potential $A_0$, generate novel contributions to the gluon self energy at $\sim g^2$. These ensure the gluon self energy remains transverse to $\sim g^2$, and are essential in computing contributions to the free energy at $\sim g^3$ for small holonomy, $\overline{A}_0 \sim T$. We show that the contribution $\sim g^3$ from off-diagonal gluons is discontinuous as the holonomy vanishes. The contribution from diagonal gluons is continuous as the holonomy vanishes, but sharply constrains the possible sources which generate nonzero holonomy, and must involve an infinite number of Polyakov loops.
Highlights
The collisions of heavy nuclei at very high energies demonstrate the existence of a qualitatively new state of matter
In this paper we have considered the behavior of the free energy at nonzero holonomy in perturbation theory, and showed that they exhibit several unexpected features
The simplest way to ensure gauge invariance is by using sources which are themselves gauge invariant
Summary
The collisions of heavy nuclei at very high energies demonstrate the existence of a qualitatively new state of matter. We use several different methods, and show that the potential is only gauge invariant in the presence of gauge invariant sources involving the Polyakov loops Because these are nonlinear functions of the gauge field, these generate new contributions to the gluon self-energy ∼g2. Understanding the behavior of a holonomous plasma is of intrinsic interest in understanding the behavior of gauge theories at nonzero temperature It is of use in developing effective theories, which can be analytically continued to compute properties near equilibrium [24,34,35,36,37,38,39]. This allows one to show that the free energy from off-diagonal contributions is continuous to ∼g4 as the holonomy vanishes
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