New solutions to the Ginsparg-Wilson equation

TL;DR

This paper introduces a new class of chiral Dirac operators with exact symmetry, demonstrating their properties and numerical behavior, though practical use may be limited due to computational costs.

Contribution

It constructs a general class of chiral Dirac operators, proves their key properties, and tests their numerical behavior, expanding theoretical understanding beyond the overlap operator.

Findings

Operators have no fermion doublers

Operators are exponentially local

Numerical tests confirm theoretical properties

Abstract

The overlap operator is just the simplest of a class of Dirac operators with an exact chiral symmetry. I demonstrate how a general class of chiral Dirac operators can be constructed, show that they have no fermion doublers and that they are all exponentially local, and test my conclusions numerically for a few examples. However, since these operators are more expensive than the overlap operator, it is unlikely that they will be useful in practical simulations.