Non-perturbative Thermodynamics of Quark Gluon Plasma and Gravitational Waves

TL;DR

This paper models the quark-gluon plasma using non-linear classical SU(2) Yang-Mills fields, computes its thermodynamics, and investigates how gravitational waves can induce instabilities within this non-perturbative framework.

Contribution

It introduces a novel non-perturbative, time-dependent background approach to study QGP thermodynamics and its interaction with gravitational waves, expanding understanding beyond perturbative methods.

Findings

Thermodynamic pressure increases with temperature, showing a logarithmic trend.

Quark back-reaction can break isotropy in the condensate under certain conditions.

Gravitational waves can induce instabilities in the quark-gluon plasma.

Abstract

Quark-Gluon Plasma (QGP), a strongly interacting state of the early universe, exhibits remarkably fluid-like behavior despite its underlying non-Abelian dynamics. Motivated by these features, we explore time-dependent SU(2) Yang-Mills condensates as non-linear classical background fields to model QGP. We first study quarks in gluon backgrounds and show that quark back-reaction can break the isotropy of the condensate for certain initial conditions. We then compute the one-loop finite-temperature effective action using the background-field method and heat-kernel expansion. The resulting thermodynamic pressure increases with temperature but exhibits an approximately logarithmic dependence. This is expected, as this is the de-confined phase of QGP; it is not exactly an ideal gas due to self-interaction. We also perform lattice calculations for the system to contrast continuum and lattice perspectives. We then add the GW to the thermodynamic QGP model and show that certain frequencies of the GW can induce instabilities in the QGP. Our analysis explores the limitations and role of non-perturbative, time-dependent backgrounds in semi-classical description of Yang-Mills dynamics.