Nonperturbative Regulator for Chiral Gauge Theories?

TL;DR

This paper introduces a nonperturbative, gauge-invariant lattice regulator for chiral gauge theories using domain wall fermions and gradient flow, potentially revealing mirror fermions with unique physical properties.

Contribution

It proposes a novel lattice regularization method for chiral gauge theories that maintains gauge invariance and addresses anomaly considerations.

Findings

The method produces a theory with gauged and mirror fermions coupled via a soft form factor.

The approach is consistent only if the chiral fermion representation is anomaly free.

Potential physical implications include the existence of invisible mirror fermions in the standard model.

Abstract

We propose a nonperturbative gauge invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d + 1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d-dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.