General Ginsparg-Wilson fermions and index

TL;DR

This paper proves that for general Ginsparg-Wilson fermions, the lattice index theorem remains valid, with geometric and algebraic zero mode eigenspaces coinciding, ensuring no extraneous contributions.

Contribution

It provides a rigorous proof that the index theorem holds for general Ginsparg-Wilson fermions without additional unwanted terms.

Findings

Geometric and algebraic zero mode eigenspaces are equal.

The lattice index theorem is preserved for general Ginsparg-Wilson fermions.

No extraneous terms spoil the index theorem on the lattice.

Abstract

We show rigorously that for general Ginsparg-Wilson fermions the dimensions of the geometric eigenspace and of the algebraic one for zero modes agree so that the index theorem on the lattice is not spoiled by unwanted additional terms.