On the continuum limit of fermionic topological charge in lattice gauge theory

TL;DR

This paper proves that the fermionic topological charge in lattice gauge theory converges to the continuum topological charge in the classical limit, confirming the consistency of lattice definitions with continuum topology.

Contribution

It establishes the continuum limit of the fermionic topological charge defined via spectral flow and the Overlap Dirac operator for SU(N) lattice gauge fields.

Findings

Fermionic topological charge reduces to continuum charge in the classical limit

Spectral flow and Overlap operator definitions are consistent with continuum topology

Validates lattice methods for topological charge calculation

Abstract

It is proved that the fermionic topological charge of SU(N) lattice gauge fields on the 4-torus, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac operator, reduces to the continuum topological charge in the classical continuum limit when the parameter $m_0$ is in the physical region $0<m_0<2$.