Field localization on a brane intersection in anti-de Sitter spacetime

TL;DR

This paper investigates the conditions under which scalar, fermion, and gauge fields can be localized on a 3-brane at the intersection of two 4-branes in anti-de Sitter space, with implications for brane world models and string theory.

Contribution

It identifies specific conditions for zero-mode localization of various fields on the intersection brane in higher-dimensional AdS geometries.

Findings

Zero modes can be localized if masses and couplings meet certain relations.

Localization is unaffected by distant 4-branes in the probe approximation.

Chiral fermion modes can be localized independently due to geometric properties.

Abstract

We discuss the localization of scalar, fermion, and gauge field zero modes on a $3-$brane that resides at the intersection of two $4-$branes in six-dimensional anti-de Sitter space. This set-up has been introduced in the context of brane world models and, higher-dimensional versions of it, in string theory. In both six- and ten-dimensional cases, it has been shown that four-dimensional gravity can be reproduced at the intersection, due to the existence of a massless, localized graviton zero-mode. However, realistic scenarios require also the Standard Model to be localized on the $3-$brane. In this paper, we discuss under which conditions a higher-dimensional field theory, propagating on the above geometry, can have a zero-mode sector localized at the intersection and find that zero modes can be localized only if masses and couplings to the background curvature satisfy certain relations. We also consider the case when other 4-branes cut the bulk at some distance from the intersection and argue that, in the probe brane approximation, there is no significant effect on the localization properties at the $3-$brane. The case of bulk fermions is particularly interesting, since the properties of the geometry allow localization of chiral modes independently.