Heavy-tailed chiral random matrix theory

TL;DR

This paper introduces a heavy-tailed chiral random matrix model that exhibits unique symmetry-breaking behavior and provides analytical solutions for spectral properties, revealing exotic phenomena like non-decoupling of heavy flavors.

Contribution

It presents a novel heavy-tailed chiral random matrix model with analytical solutions for spectral densities and eigenvalue distributions, highlighting unconventional behaviors.

Findings

Chiral symmetry breaking without bilinear condensate

Analytical spectral density and eigenvalue distribution derived

Exotic phenomena such as non-decoupling and power-law tails observed

Abstract

We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.