Non-perturbative Thermodynamics of Quark Gluon Plasma and Gravitational Waves

TL;DR

The study investigates non-perturbative, time-dependent SU(2) Yang–Mills condensates as background fields to model the quark–gluon plasma (QGP) at finite temperature. It combines a quark–gluon condensate framework with the background-field method and heat-kernel expansion to compute the one-loop thermodynamic potential, revealing non-ideal pressure behavior that grows logarithmically with temperature due to a dominant classical action density. By contrasting continuum results with lattice calculations and extending the model to include gravitational waves, the work identifies GW-induced instabilities at certain frequencies and demonstrates how fluctuations and backreaction modify the background and the resulting thermodynamics. The findings emphasize the limitations and utility of non-perturbative, time-dependent backgrounds in semi-classical YM dynamics and point to future work integrating SU(3), Polyakov-loop dynamics, and more complete lattice analyses. Overall, the paper provides a framework for connecting non-perturbative YM structures with finite-temperature QGP thermodynamics and possible GW interactions in early-universe contexts.

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.

Figures (15)

• Figure 1: Figure showing the numerical solutions for diagonal components of the gauge field for a short amount of time. The Red, Blue and Green plots corresponds to $\tilde{A}^a_a$, $\tilde{A}^1_1 =\tilde{A}^2_2$ and $\tilde{A}^3_3$, respectively. We choose $g_{ym}=0.1$, $c_1=1$ with initial conditions $\tilde{A}^a_a(0) = \partial_t \tilde{A}^a_a(0) =0$.
• Figure 2: Figure showing the numerical solutions for diagonal components of the gauge field. The Red, Blue and Green plots corresponds to $\tilde{A}^a_a$, $\tilde{A}^1_1=\tilde{A}^2_2$ and $\tilde{A}^3_3$, respectively.The dashed plots corresponds to the initial conditions $\tilde{A}^a_a(0) = \partial_t \tilde{A}^a_a(0) =0$ and the thick lines corresponds to $\tilde{A}^a_a(0) =0$, $\partial_t \tilde{A}^a_a(0) =1$. We choose $g_{ym}=0.1$ and $c_1=1$.
• Figure 3: Figures showing the thermodynamic potential $\Omega$ as a function of $c_1$ and temperature $T$. For this, we set $\Lambda_{\bar{MS}} = 200$ MeV.
• Figure 4: Figures showing the normalized pressure as a function of temperature $T/T_c$. For this, we set $N=2$, $N_f =2$ and $\Lambda_{\bar{MS}} = 200$ MeV.
• Figure 5: Comparison plot of normalised pressure with ${\rm Log} (T/T_c)$.