Quantifying non-invertible chiral symmetry breaking

Abstract

It has recently been suggested that the chiral symmetry of the Standard Model is not explicitly broken by its ABJ anomaly, but is instead made non-invertible. In this work, I quantify the breaking of non-invertible symmetries of this type by calculating the symmetry breaking scales and effective charges $q(r)$ originally studied for continuous invertible higher-form symmetries. As an example I consider the explicit breaking of the chiral symmetry of massless QED by introducing Yukawa couplings between the electron and a massive real scalar in the UV. I briefly comment on how one might quantify the breaking of general non-invertible symmetries.