Four-dimensional lattice chiral gauge theories with anomalous fermion content

TL;DR

This paper introduces a lattice framework for studying four-dimensional chiral gauge theories with anomalous fermion content non-perturbatively, incorporating gauge boson mass terms and Wess-Zumino-Witten terms.

Contribution

It presents a novel lattice formulation enabling non-perturbative analysis of anomalous chiral gauge theories with a consistent fermion measure.

Findings

Constructed a lattice fermion measure satisfying the Ginsparg-Wilson relation.

Provides a method to determine the UV cutoff in low-energy effective theories.

Defines a lattice non-linear sigma model with Wess-Zumino-Witten term.

Abstract

In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to acquire mass. Such theories in four dimensions are inevitablly non-renormalizable and must be regarded as a low-energy effective theory with a finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework which enables one to study such theories in a non-perturbative level. By introducing bare mass terms of gauge bosons that impose ``smoothness'' on the link field, we explicitly construct a consistent fermion integration measure in a lattice formulation based on the Ginsparg-Wilson (GW) relation. This framework may be used to determine in a non-perturbative level an upper bound on the UV cutoff in low-energy effective theories with anomalous fermion content. By further introducing the St\"uckelberg or Wess-Zumino (WZ) scalar field, this framework provides also a lattice definition of a non-linear sigma model with the Wess-Zumino-Witten (WZW) term.