Investigation of the Domain Wall Fermion Approach to Chiral Gauge Theories on the Lattice

TL;DR

This paper explores the use of domain wall fermions to formulate chiral gauge theories on the lattice, focusing on finite volume effects, gauge invariance, and the decoupling of mirror modes, with numerical evidence suggesting the absence of a strong coupling symmetric phase.

Contribution

It provides a detailed investigation of domain wall fermions for chiral gauge theories, highlighting challenges in decoupling mirror modes and the non-existence of a strong coupling symmetric phase.

Findings

Extra light modes do not decouple in the expected phase.

Numerical results suggest the strong coupling symmetric phase is unlikely.

The approach faces fundamental obstacles in constructing anomaly-free chiral theories.

Abstract

We investigate a recent proposal to construct chiral gauge theories on the lattice using domain wall fermions. We restrict ourselves to the finite volume case, in which two domain walls are present, with modes of opposite chirality on each of them. We couple the chiral fermions on only one of the domain walls to a gauge field. In order to preserve gauge invariance, we have to add a scalar field, which gives rise to additional light mirror fermion and scalar modes. We argue that in an anomaly free model these extra modes would decouple if our model possesses a so-called strong coupling symmetric phase. However, our numerical results indicate that such a phase most probably does not exist. ---- Note: 9 Postscript figures are appended as uuencoded compressed tar file.