Generalized Ginsparg-Wilson relations

TL;DR

This paper derives generalized Ginsparg-Wilson relations applicable to Dirac and Majorana fermions across dimensions, elucidating their role in encoding anomalies and symmetries in lattice formulations of topological phases.

Contribution

It provides a comprehensive derivation of Ginsparg-Wilson relations for various fermions and links them to anomalies and symmetries in lattice quantum field theories.

Findings

Formulation of exact lattice symmetries for fermions.

Connection between Ginsparg-Wilson relations and anomalies.

Application to topological insulators and superconductors.

Abstract

We give a general derivation of Ginsparg-Wilson relations for both Dirac and Majorana fermions in any dimension. These relations encode continuous and discrete chiral, parity and time reversal anomalies and will apply to the various classes of free fermion topological insulators and superconductors (in the framework of a relativistic quantum field theory in Euclidean spacetime). We show how to formulate the exact symmetries of the lattice action and the relevant index theorems for the anomalies.