Connecting dilaton thermal fluctuation with the Polyakov loop at finite temperature

TL;DR

This paper derives a formula linking the Polyakov loop expectation value to dilaton fluctuations at finite temperature, matching lattice data and predicting a strong first-order phase transition at large N_c, thus connecting deconfinement and scale symmetry.

Contribution

It introduces a new formula for the Polyakov loop expectation value based on the effective potential and relates dilaton fluctuations to deconfinement, advancing understanding of phase transitions in gauge theories.

Findings

Agreement with lattice QCD data

Prediction of a strong first-order transition at large N_c

Relation between dilaton fluctuations and deconfinement

Abstract

Understanding the character of the deconfinement phase transition is one of the fundamental challenges in particle physics. In this work, we derive a formula for the expectation value of the Polyakov loop -- the order parameter of the deconfinement phase transition -- in pure $\mathrm{SU(N_{\mathrm{c}})}$ gauge systems at finite temperatures starting from the Coleman\textendash Weinberg-type effective potential encoding the trace anomaly of QCD. Our results are in good agreement with the Lattice QCD data and can effectively describe the large-$N_{\mathrm{c}}$ behaviors of the expectation value of the Polyakov loop. Notably, our findings predict the strongest first-order deconfinement phase transition as $N_{\mathrm{c}} \to +\infty$. Furthermore, to establish a relation between the dilaton field and the Polyakov loop, we also derive the scale transformation rule for temperature based on quantum statistical mechanics. The results of this work may shed a light on the connection between deconfinement phase transition and evolution of scale symmetry in the thermal system.