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The Dimensional-Reduction Anomaly in Spherically Symmetric Spacetimes

P. Sutton
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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.

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P. Sutton. 2000-04-30. The Dimensional-Reduction Anomaly in Spherically Symmetric Spacetimes. https://doi.org/10.1103/physrevd.62.044033

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