Fermionic topological charge of families of lattice gauge fields

TL;DR

This paper defines the topological charge for families of lattice gauge fields using fermionic methods, linking index theory and gauge invariance issues in lattice gauge theory.

Contribution

It introduces a fermionic definition of topological charge for lattice gauge fields based on families index theory, connecting topological and gauge invariance obstructions.

Findings

Fermionic topological charge is characterized via families index theory.

Obstructions to gauge invariance are naturally described in this framework.

Links between topological charge and gauge fixing issues are established.

Abstract

Topological charge of families of lattice gauge fields is defined fermionically via families index theory for the overlap Dirac operator. Certain obstructions to gauge invariance of the overlap chiral fermion determinant, as well as the lattice analogues of certain obstructions to gauge fixings without the Gribov problem, have natural descriptions in this context.