Condensation and prescaling in spatial Polyakov loop correlations far from equilibrium

TL;DR

This paper studies the far-from-equilibrium behavior of spatial Polyakov loop correlations in SU(N) gauge theories, revealing condensate formation and energy cascades, with implications for understanding gluon plasma dynamics.

Contribution

It demonstrates the formation of a condensate and prescaling behavior in Polyakov loop correlations, supported by lattice simulations and perturbative analysis, extending understanding of nonthermal attractors.

Findings

Condensate forms at zero momentum mode.

Energy cascades toward ultraviolet at nonzero momenta.

No inverse cascade observed above electric screening scale.

Abstract

The far-from-equilibrium dynamics of spatial Polyakov loop correlations, which provide gauge-invariant observables akin to effective particle numbers for gluon plasmas, are investigated within real-time $\mathrm{SU}(N_c)$ lattice gauge theory at weak couplings and large gluon occupations. The momentum zero mode of these correlations reveals the dynamic formation of a condensate, while at nonzero momenta, energy is transported toward the ultraviolet. We demonstrate that the non-zero momentum dynamics is well described by a direct cascade in terms of gauge-invariant Polyakov loop excitations, exhibiting self-similar prescaling indicative of a nonthermal attractor. This behavior can be analytically understood through perturbation theory for the Polyakov loop correlations and the established dynamics of gauge field correlations. We perform simulations for both $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ gauge groups, providing further consistency checks on the $N_c$-dependence of perturbative expectations. No evidence of an inverse cascade toward lower momenta is found for momenta above the electric screening scale.