The Dimensional-Reduction Anomaly in Spherically Symmetric Spacetimes

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. However, it has been shown 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.