Gapped Chiral Fermions

TL;DR

The paper tackles the problem of gapping massless fermions while preserving global chiral symmetries, which is obstructed by ’t Hooft anomalies. It introduces a continuum strategy based on s-confinement in supersymmetric gauge theories, coupling the chiral fermions to auxiliary vector-like sectors and allowing relevant IR mass terms to emerge without breaking the symmetry $G$. It provides concrete constructions, including gapping a Standard Model-like generation and achieving mod 16 anomaly-consistent gapping for 16 Weyl fermions under Spin-${\bf Z}_4$, plus a 2+1D time-reversal case via dimensional reduction. The work also discusses robustness to soft SUSY breaking and outlines broad generalizations to other s-confining theories, highlighting a versatile framework for symmetric mass generation in diverse chiral settings.

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.