Exact Zero-Modes of the Compact QED Dirac Operator

TL;DR

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

Contribution

It provides the first calculation of exact zero-modes in compact QED and links these to topological excitations, extending understanding from non-Abelian to Abelian gauge theories.

Findings

Exact zero-modes found in strong coupling phase

Similarity of zero-modes to non-Abelian lattice QCD

Initial identification of topological excitations responsible

Abstract

We calculate the low-lying eigenmodes of the Neuberger overlap-Dirac operator for $4d$ compact lattice QED in the quenched approximation. In the strong coupling phase we find exact zero-modes, quite similar as in non-Abelian lattice QCD. Subsequently we make an attempt to identify responsible topological excitations of the U(1) lattice gauge theory.