Local Fields on the Brane Induced by Nonlocal Fields in the Bulk

TL;DR

This paper explores how nonlocal bulk fields influence local fields on a brane in quantum field theory, analyzing their properties in flat and anti-de Sitter backgrounds and their implications for renormalizability and symmetries.

Contribution

It introduces a framework where bulk fields are nonlocal while brane fields remain local, and studies their ultraviolet behavior and conformal invariance.

Findings

Constructed a family of nonlocal bulk fields with local brane counterparts.

Identified subfamilies leading to renormalizable brane theories.

Analyzed the relation between bulk and brane conserved currents.

Abstract

We investigate quantum field theory in a bulk space with boundary, which represents a 3-brane. Both flat and anti-de Sitter backgrounds are considered. The basic idea is to keep local commutativity only on the brane, giving up this requirement in the bulk. We explore the consequences of this proposal, constructing a large family of nonlocal bulk fields, whose brane relatives are local. We estimate the ultraviolet behavior of these local brane fields, characterizing a subfamily which generates renormalizable theories on the brane. The issue of brane conformal invariance and the relation between bulk and brane conserved currents are also examined in this framework.