A Chiral Solution to the Ginsparg-Wilson Equation

TL;DR

This paper introduces a new chiral solution to the Ginsparg-Wilson equation using a five-dimensional domain wall fermion approach, enabling nonperturbative regulation of chiral gauge theories.

Contribution

It provides a novel derivation of a four-dimensional chiral overlap operator satisfying the Ginsparg-Wilson equation through a five-dimensional framework.

Findings

Derived an effective four-dimensional chiral overlap operator.

Showed the operator obeys the Ginsparg-Wilson equation.

Reproduces properties of continuum chiral gauge theories.

Abstract

We present a chiral solution of the Ginsparg-Wilson equation. This work is motivated by our recent proposal for nonperturbatively regulating chiral gauge theories, where five-dimensional domain wall fermions couple to a four-dimensional gauge field that is extended into the extra dimension as the solution to a gradient flow equation. Mirror fermions at the far surface decouple from the gauge field as if they have form factors that become infinitely soft as the distance between the two surfaces is increased. In the limit of an infinite extra dimension we derive an effective four-dimensional chiral overlap operator which is shown to obey the Ginsparg-Wilson equation, and which correctly reproduces a number of properties expected of chiral gauge theories in the continuum.