The Dimensional-Reduction Anomaly in Spherically Symmetric Spacetimes

TL;DR

This paper investigates the dimensional-reduction anomaly in spherically symmetric spacetimes, revealing how renormalization disrupts the expected relationship between higher-dimensional fields and their dimensionally reduced counterparts.

Contribution

It provides an analysis of the dimensional-reduction anomaly specifically in spherically symmetric spaces, highlighting the effects of renormalization on this phenomenon.

Findings

Renormalization breaks the relationship between D-dimensional and reduced theories.

The anomaly is significant in spherically symmetric spacetimes.

The study clarifies the impact of the anomaly on quantum field decomposition.

Abstract

In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces, reducing the system to a collection of (D-n)-dimensional fields. This allows one to write bare D-dimensional field quantities like the Green function and the effective action as sums of their (D-n)-dimensional counterparts in the dimensionally reduced theory. It has been shown, however, that renormalization breaks this relationship between the original and dimensionally reduced theories, an effect called the dimensional-reduction anomaly. We examine the dimensional-reduction anomaly for the important case of spherically symmetric spaces.