Warped Domain Wall Fermions

TL;DR

This paper explores warped domain wall fermions in an AdS background, demonstrating how chiral gauge theories can emerge from vector-like theories through specific limits and numerical verification.

Contribution

It introduces a method to realize chiral gauge theories using warped domain wall fermions in AdS space, analyzing gauge invariance restoration and numerical verification of the approach.

Findings

Heavy Kaluza-Klein modes in the limit approach a chiral gauge theory

Gauge invariance restored by infinite extra dimension length or zero AdS curvature

Numerical verification supports the classical limit approximation

Abstract

We consider Kaplan's domain wall fermions in the presence of an Anti-de Sitter (AdS) background in the extra dimension. Just as in the flat space case, in a completely vector-like gauge theory defined after discretizing this extra dimension, the spectrum contains a very light charged fermion whose chiral components are localized at the ends of the extra dimensional interval. The component on the IR boundary of the AdS space can be given a large mass by coupling it to a neutral fermion via the Higgs mechanism. In this theory, gauge invariance can be restored either by taking the limit of infinite proper length of the extra dimension or by reducing the AdS curvature radius towards zero. In the latter case, the Kaluza-Klein modes stay heavy and the resulting classical theory approaches a chiral gauge theory, as we verify numerically. Potential difficulties for this approach could arise from the coupling of the longitudinal mode of the light gauge boson, which has to be treated non-perturbatively.