The Effect of Dynamical Gauge Field on the Chiral Fermion on a boundary

TL;DR

This paper investigates how dynamical gauge fields influence the chiral fermion boundary states in a higher-dimensional setup, revealing that gauge dynamics destroy the fermion's chiral properties despite perturbative indications of their survival.

Contribution

It provides an exact non-perturbative proof that gauge field dynamics eliminate boundary fermion chirality in the strong coupling limit.

Findings

Boundary fermion chirality is destroyed by gauge dynamics.

Exact parity invariance of the fermion propagator is proven.

Chiral properties do not survive in the strong gauge coupling limit.

Abstract

We study the effect of dynamical gauge field on the Kaplan's chiral fermion on a boundary in the strong gauge coupling limit in the extra dimension. To all orders of the hopping parameter expansion, we prove exact parity invariance of the fermion propagator on the boundary. This means that the chiral property of the boundary fermion, which seems to survive even in the presence of the gauge field from a perturbative point of view, is completely destroyed by the dynamics of the gauge field.