The Role of Initial Conditions in Presence of Extra Dimensions

TL;DR

This paper investigates how initial conditions in a 5D bulk space influence quantum field behavior on a 3-brane, revealing a variety of fields including some with ultraviolet finiteness similar to string theories.

Contribution

It demonstrates that initial conditions in the bulk determine the Kaluza-Klein measure and introduces a classification of quantum fields on the brane arising from different bulk initial conditions.

Findings

Initial conditions affect the Kaluza-Klein measure.

Existence of a rich family of quantum fields on the brane.

Some fields are ultraviolet finite and share features with string theories.

Abstract

Quantum field theory in 4+1 dimensional bulk space with boundary, representing a 3-brane, is considered. We study the impact of the initial conditions in the bulk on the field dynamics on the brane. We demonstrate that these conditions determine the Kaluza-Klein measure. We also establish the existence of a rich family of quantum fields on the brane, generated by the same bulk action, but corresponding to different initial conditions. A simple classification of these fields is proposed and it is shown that some of them lead to ultraviolet finite theories, which have some common features with strings.