Field Configurations and their Instability Induced by Higher Dimensions of Spacetime: An Example

TL;DR

This paper investigates the stability of scalar field configurations in a 5-dimensional spacetime model, revealing how topology and interactions induce instabilities and energy differences that affect the extra dimension's stability.

Contribution

The study identifies two types of scalar field configurations and analyzes how their interactions and topological properties lead to instabilities and distinguishability of branes in higher-dimensional models.

Findings

Untwisted field becomes unstable due to one-loop corrections.

Twisted field causes energy differences between branes.

Fifth dimension stability is compromised by field interactions.

Abstract

We use the model of L. Randall et al to investigate the stability of allowed quantum field configurations. Firstly, we find that due to the topology of this 5 dimensional model, there are 2 possible configurations of the scalar field, untwisted and twisted. They give rise to two types of instability. Secondly, when allowed to interact in the 3-brane, the untwisted field becomes unstable even if it is at the true vacuum groundstate.This instability in the 4D submanifold results results from one-loop corrections that arise from coupling with the twisted field. On the other hand, the twisted field can make the two 3-branes distinguishable by causing an energy difference between them. That is due to the antiperiodicity of the twisted fields, when rotating with $\pi$ to go from one 3-brane to the other. The energy difference between the branes renders the fifth dimension unstable.