The gradient flow of the Dirac spectrum

TL;DR

This paper develops a theoretical framework for understanding how the microscopic Dirac eigenvalues evolve under gradient flow, revealing that eigenvalue repulsion diminishes with flow time and comparing spectral flow to chiral condensate flow.

Contribution

It introduces a chiral perturbation theory for the gradient flow of microscopic Dirac eigenvalues and analyzes their spectral correlations at different flow times.

Findings

Eigenvalue repulsion decreases with increasing flow time

Spectral resolvent flow is comparable to chiral condensate flow

Provides analytical predictions for eigenvalue distributions under flow

Abstract

We construct chiral perturbation theory for the gradient flow of the microscopic Dirac eigenvalues and compute the density of and correlations between the microscopic eigenvalues at zero and non-zero flow time. The results show that the repulsion of the microscopic Dirac eigenvalues from the dynamical quark mass decreases with increasing gradient flow time. Furthermore, the flow of the spectral resolvent is compared to the flow of the chiral condensate obtained from a fermionic gradient flow.