The Dimensional-Reduction Anomaly

Preprint

9 October 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.hep-th/9909086

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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All Related Versions

Version 1, 1999-09-13, ArXiv
Version 2, 1999-09-22, ArXiv
Version 3, 1999-10-09, ArXiv
Published version: Physical Review D, 61 (2), 024021.

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