Order parameters for gauge invariant condensation far from equilibrium

TL;DR

This paper investigates gauge condensation in high-energy nuclear collisions, identifying gauge-invariant order parameters and demonstrating condensate formation through real-time lattice simulations, with potential implications for early heavy ion collision dynamics.

Contribution

It introduces gauge-invariant observables as order parameters for gauge condensation and demonstrates their behavior in far-from-equilibrium SU(2) gauge theory simulations.

Findings

Gauge condensation occurs with a system-size dependent timescale.

Two gauge-invariant correlators serve as order parameters.

Universal scaling exponent describes condensate formation time.

Abstract

Nuclear collisions at sufficiently high energies are expected to produce far-from-equilibrium matter with a high density of gluons at early times. We show gauge condensation, which occurs as a consequence of the large density of gluons. To identify this condensation phenomenon, we construct two local gauge-invariant observables that carry the macroscopic zero mode of the gauge condensate. The first order parameter for gauge condensation investigated here is the correlator of the spatial Polyakov loop. We also consider, for the first time, the correlator of the gauge invariant scalar field, associated to the exponent of the Polyakov loop. Using real-time lattice simulations of classical-statistical $SU(2)$ gauge theory, we find gauge condensation on a system-size dependent time scale $t_{\text{cond}} \sim L^{1/\zeta}$ with a universal scaling exponent $\zeta$. Furthermore, we suggest an effective theory formulation describing the dynamics using one of the order parameters identified. The formation of a condensate at early times may have intriguing implications for the early stages in heavy ion collisions.