Meron Pairs and Fermion Zero Modes

TL;DR

This paper constructs a smooth, finite action lattice solution for meron pairs in QCD, derives their zero modes analytically, and proposes using these zero modes to identify merons in lattice QCD simulations.

Contribution

It introduces a new smooth lattice solution for meron pairs and analytically derives their zero modes, aiding in their identification in QCD studies.

Findings

Constructed a finite action lattice solution for meron pairs.

Derived analytical zero modes matching lattice solutions.

Proposed zero mode analysis as a tool for detecting merons in QCD simulations.

Abstract

Merons, conjectured as a semiclassical mechanism for color confinement in QCD, have been described analytically by either infinite action configurations or an Ansatz with discontinuous action. We construct a smooth, finite action, stationary lattice solution corresponding to a meron pair. We also derive an analytical solution for the zero mode of the meron pair Ansatz, show that it has the qualitative behavior of the exact zero mode of the lattice solution, and propose the use of zero modes to identify meron gauge field configurations in stochastic evaluations of the lattice QCD path integral.