Gapped Chiral Fermions

TL;DR

This paper demonstrates methods to gap chiral fermions while preserving symmetries, using supersymmetric gauge theories and confinement phenomena, with implications for Standard Model fermions and discrete anomalies.

Contribution

It introduces models that gap chiral fermions without symmetry breaking, leveraging supersymmetric dynamics and confinement, advancing understanding of anomaly-preserving fermion gapping.

Findings

Gapped fermions with Standard Model quantum numbers without electroweak symmetry breaking.

Achieved fermion gapping in groups of 16 with discrete symmetry preservation.

Utilized supersymmetric gauge theories and confinement phenomena for fermion gapping.

Abstract

In principle, there is no obstacle to gapping fermions preserving any global symmetry that does not suffer a 't Hooft anomaly. In practice, preserving a symmetry that is realised on fermions in a chiral manner necessitates some dynamics beyond simple quadratic mass terms. We show how this can be achieved using familiar results about supersymmetric gauge theories and, in particular, the phenomenon of confinement without chiral symmetry breaking. We present simple models that gap fermions while preserving a symmetry group under which they transform in chiral representations. For example, we show how to gap a collection of 4d fermions that carry the quantum numbers of one generation of the Standard Model, but without breaking electroweak symmetry. We further show how to gap fermions in groups of 16 while preserving certain discrete symmetries that exhibit a mod 16 anomaly.