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arXiv · hep-th/9909086

The Dimensional-Reduction Anomaly

V. Frolov·P. Sutton·A. Zelnikov
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Abstract

In a wide class of D-dimensional spacetimes which are direct or semi-direct sums of a (D-n)-dimensional space and an n-dimensional homogeneous ``internal'' space, a field can be decomposed into modes. As a result of this mode decomposition, the main objects which characterize the free quantum field, such as Green functions and heat kernels, can effectively be reduced to objects in a (D-n)-dimensional spacetime with an external dilaton field. We study the problem of the dimensional reduction of the effective action for such spacetimes. While before renormalization the original D-dimensional effective action can be presented as a ``sum over modes'' of (D-n)-dimensional effective actions, this property is violated after renormalization. We calculate the corresponding anomalous terms explicitly, illustrating the effect with some simple examples.

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V. Frolov, P. Sutton, A. Zelnikov. 1999-10-09. The Dimensional-Reduction Anomaly. https://doi.org/10.1103/physrevd.61.024021

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