Zero-modes of the QED Neuberger Dirac operator

TL;DR

This paper investigates the low-lying eigenmodes of the Neuberger overlap-Dirac operator in 4D lattice QED, revealing exact zero-modes in the strong coupling phase and exploring their topological implications.

Contribution

It provides the first detailed analysis of zero-modes of the Neuberger operator in lattice QED and discusses their relation to topological excitations.

Findings

Exact zero-modes found in the strong coupling phase

Connection established between zero-modes and topological excitations

Comparison with random matrix theory spectrum

Abstract

We consider $4d$ compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying eigenmodes of the Neuberger overlap-Dirac operator. In the strong coupling phase we find exact zero-modes. Subsequently we discuss possibly related topological excitations of the U(1) lattice gauge theory.