Adding Gauge Fields to Kaplan's Fermions

TL;DR

This paper explores adding dynamical gauge fields to Kaplan fermions, demonstrating correct 2d gauge dynamics, chiral fermion behavior, and anomaly consistency through simulations involving a Higgs mechanism and boundary mode analysis.

Contribution

It introduces a method to incorporate dynamical gauge fields into Kaplan fermions and verifies their correct chiral and anomaly properties via numerical simulations.

Findings

3d gauge theory produces correct 2d gauge dynamics

Fermion propagators exhibit proper chiral structure

Boundary modes are non-chiral and decoupled

Abstract

We experiment with adding dynamical gauge field to Kaplan (defect) fermions. In the case of U(1) gauge theory we use an inhomogenous Higgs mechanism to restrict the 3d gauge dynamics to a planar 2d defect. In our simulations the 3d theory produce the correct 2d gauge dynamics. We measure fermion propagators with dynamical gauge fields. They posses the correct chiral structure. The fermions at the boundary of the support of the gauge field (waveguide) are non-chiral, and have a mass two times heavier than the chiral modes. Moreover, these modes cannot be excited by a source at the defect; implying that they are dynamically decoupled. We have also checked that the anomaly relation is fullfilled for the case of a smooth external gauge field. This is an uuencoded ps-file. Use 'uudecode hepchiral.ps.Z' and 'uncompress hepchiral.ps.Z' to produce the psfile.