A geometric approach to correlations and quark number susceptibilities

TL;DR

This paper introduces a geometric framework for analyzing thermodynamic properties of hot QCD near the critical temperature, linking it with microscopic quantities like quark-number susceptibility, and incorporating thermal fluctuations.

Contribution

It develops a geometric approach to QCD thermodynamics that relates macroscopic geometry with microscopic susceptibilities, applicable in perturbative and potentially non-perturbative regimes.

Findings

Established a geometric interpretation of quark susceptibilities.

Linked thermodynamic geometry with microscopic QCD quantities.

Incorporated thermal fluctuations into the geometric analysis.

Abstract

We study the thermodynamic geometry arising from the free energy for the 2- and 3-flavor finite temperature hot QCD near the critical temperature. We develop a geometric notion for QCD thermodynamics, relating it with the existing microscopic quantities, e.g. quark-number susceptibility, which appears naturally within an approximately self-consistent resummation of perturbative QCD. We further incorporate thermal fluctuations in the free energy, thus yielding the geometric properties of local and global chemical correlations. These investigations are perturbative in nature. Nevertheless, one could apply the same line of thought for the geometric realization of underlying quark susceptibilities, either in the fabric of lattice QCD or in that of non-perturbative QCD.