Lattice chirality and the decoupling of mirror fermions

TL;DR

This paper demonstrates that lattice gauge theories with chiral fermions can be split into light and mirror sectors only if both are anomaly-free, clarifying how mirror fermions can be decoupled without breaking gauge symmetry.

Contribution

It provides a rigorous framework for splitting lattice gauge theories into chiral sectors using exact lattice chirality, emphasizing the importance of anomaly cancellation for a smooth spectrum.

Findings

Partition functions can be split into light and mirror parts only if both are anomaly free.

Mirror sector spectrum is smooth and well-defined only under anomaly-free conditions.

The results clarify the decoupling of mirror fermions in lattice gauge theories.

Abstract

We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into "light" and "mirror" parts, such that the "light" and "mirror" representations are chiral. The splitting of the full partition function into "light" and "mirror" is well defined only if the two sectors are separately anomaly free. We show that only then is the generating functional, and hence the spectrum, of the mirror theory a smooth function of the gauge field background. This explains how ideas to use additional non-gauge, high-scale mirror-sector dynamics to decouple the mirror fermions without breaking the gauge symmetry--for example, in symmetric phases at strong mirror Yukawa coupling--are forced to respect the anomaly-free condition when combined with the exact lattice chiral symmetry. Our results also explain a paradox posed by a recent numerical study of the mirror-fermion spectrum in a toy would-be-anomalous two-dimensional theory. In passing, we prove some general properties of the partition functions of arbitrary chiral theories on the lattice that should be of interest for further studies in this field.