Multicritical Microscopic Spectral Correlators of Hermitian and Complex Matrices

TL;DR

This paper derives universal microscopic spectral densities and correlators for multicritical Hermitian and complex matrices, proposing their relevance to Dirac operators in theories lacking spontaneous chiral symmetry breaking.

Contribution

It introduces new universality classes for microscopic spectral densities in multicritical matrix ensembles and suggests their applicability to certain quantum field theories.

Findings

Derived microscopic spectral densities and correlators for multicritical ensembles

Established universality of these spectral features across different matrix types

Proposed relevance to Dirac operators in specific theoretical contexts

Abstract

We find the microscopic spectral densities and the spectral correlators associated with multicritical behavior for both hermitian and complex matrix ensembles, and show their universality. We conjecture that microscopic spectral densities of Dirac operators in certain theories without spontaneous chiral symmetry breaking may belong to these new universality classes.