The Dimensional-Reduction Anomaly in Spherically Symmetric Spacetimes

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.

LaTeX, 19 pages, 2 figures. v2: calculations simplified, references added

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• Vacuum polarization in the Schwarzschild spacetime and dimensional reduction
• Vacuum polarization in two-dimensional static spacetimes and dimensional reduction
• Discrete Symmetries of Functional Determinants
• On the Dimensional Reduction Procedure
• Long time black hole evaporation with bounded Hawking flux
• Virtual black hole phenomenology from 2d dilaton theories