Dimensional reduction of quantum fields on a brane

TL;DR

This paper investigates how restricting a quantum field to a lower-dimensional submanifold in a curved space can induce effective lower-dimensional quantum behavior due to background singularities.

Contribution

It demonstrates that singular background metrics can cause a quantum field restricted to a submanifold to behave as a lower-dimensional quantum field, revealing a new mechanism for dimensional reduction.

Findings

Restricted fields retain original singularities

Singular metrics induce lower-dimensional behavior

Potential implications for brane-world models

Abstract

If we restrict a quantum field defined on a regular D dimensional curved manifold to a d dimensional submanifold then the resulting field will still have the singularity of the original D dimensional model. We show that a singular background metric can force the restricted field to behave as a d dimensional quantum field.