Chaos in QCD? Gap equations and their fractal properties

TL;DR

This paper explores how solutions to QCD gap equations at finite chemical potential exhibit chaotic behavior and fractal structures, potentially linking chaos to confinement and phase transitions.

Contribution

It reveals the presence of chaotic and non-chaotic domains in QCD gap solutions and suggests a connection between chaos and confinement mechanisms.

Findings

Chaotic behavior appears at the transition between broken and restored chiral symmetry.

Fractal structures determine the dynamical energy cutoff for quark dispersion relations.

Chaotic dynamics may be related to the nature of confinement and deconfinement in QCD.

Abstract

We discuss how iterative solutions of QCD inspired gap-equations at finite chemical potential show domains of chaotic behavior as well as non-chaotic domains which represent one or the other of the only two -- usually distinct -- positive mass gap solutions with broken or restored chiral symmetry, respectively. In the iterative approach gap solutions exist which exhibit restored chiral symmetry beyond a certain dynamical cut-off energy. A chirally broken, non-chaotic domain with no emergent mass poles and hence with no quasi-particle excitations exists below this energy cutoff. The transition domain between these two energy separated domains is chaotic. As a result, the dispersion relation is that of quarks with restored chiral symmetry, cut at a dynamical energy scale, determined by fractal structures. We argue that the chaotic origin of the infrared cut-off could hint at a chaotic nature of confinement and the deconfinement phase transition.