Chiral anomalies and Wilson fermions

TL;DR

This paper discusses how Wilson fermions in lattice gauge theory model chiral anomalies, focusing on the eigenvalue structure of the Dirac operator and its role in topological sector transitions.

Contribution

It provides a unified description of chiral anomalies using the eigenvalue behavior of the Wilson Dirac operator in lattice gauge theory.

Findings

Eigenvalues form complex pairs or real eigenvalues with specific chirality.

Eigenvalue collisions occur outside the perturbative region.

These collisions facilitate transitions between topological sectors.

Abstract

The Wilson formulation of fermions in lattice gauge theory provides a unified description of the chiral anomalies in the standard model. The discrete Dirac operator diagonalizes into a series of two by two blocks. In each block the possible eigenvalues either form a complex pair or separate into two real eigenvalues that have specific chirality. The collision of these pairs of eigenvalues occurs outside the perturbative region and provides a path between topological sectors.