On the decoupling of mirror fermions

TL;DR

This paper investigates whether mirror fermions in lattice chiral gauge theories can decouple, finding evidence that they remain massless in the continuum limit, which challenges the idea of decoupling in such models.

Contribution

The study provides nonperturbative evidence that mirror fermions do not decouple in the 3-4-5 lattice model, highlighting the persistence of massless charged modes in the mirror sector.

Findings

Polarization tensor shows a nonzero directional discontinuity in the continuum limit.

Similar behavior observed in free massless Ginsparg-Wilson fermions.

Supports the conclusion that mirror fermions remain massless and do not decouple.

Abstract

An approach to the formulation of chiral gauge theories on the lattice is to start with a vector-like theory, but decouple one chirality (the "mirror" fermions) using strong Yukawa interactions with a chirally coupled "Higgs" field. While this is an attractive idea, its viability needs to be tested with nonperturbative studies. The model that we study here, the so-called "3-4-5" model, is anomaly free and the presence of massless states in the mirror sector is not required by anomaly matching arguments, in contrast to the "1-0" model that was studied previously. We have computed the polarization tensor in this theory and find a directional discontinuity that appears to be nonzero in the limit of an infinite lattice, which is equivalent to the continuum limit at fixed physical volume. We show that a similar behavior occurs for the free massless Ginsparg-Wilson fermion, where the polarization tensor is known to have a directional discontinuity in the continuum limit. We thus find support for the conclusion that in the continuum limit of the 3-4-5 model, there are massless charged modes in the mirror sector so that it does not decouple from the light sector. The value of the discontinuity we obtain allows for two interpretations: either a chiral gauge theory does not emerge and mirror-sector fermions in a chiral anomaly free representation remain massless, or a massless vectorlike mirror fermion appears. We end by discussing some questions for future study.