Low-lying Dirac eigenmodes and monopoles in 4D compact QED

TL;DR

This paper investigates the behavior of low-lying Dirac eigenmodes and their relation to monopoles in 4D compact QED, revealing universal anti-correlations and spectral transitions that shed light on the chiral phase transition.

Contribution

It provides a detailed analysis of Dirac eigenmodes and monopole correlations in 4D compact QED using lattice simulations and the overlap formalism, highlighting universal patterns and spectral transitions.

Findings

Near-zero modes anti-correlate with monopole currents

Spectral level spacing shows Wigner-Poisson transition

Possible implications for chiral phase transition

Abstract

We study the properties of low-lying Dirac modes in quenched compact QED at $\beta$=0.99, 1.01 and 1.03, employing $12^3\times 12$ lattices and the overlap formalism for the fermion action. We pay special attention to the spatial distributions of the low-lying Dirac modes. Near-zero modes are found to have universal anti-correlations with monopole currents below/above the critical $\beta$. We also study the nearest-neighbor level spacing distribution of Dirac eigenvalues and find a signal of a Wigner-Poisson transition. We make a possible speculation on the chiral phase transition in 4D compact QED.