The Dimensional-Reduction Anomaly

Details The Dimensional-Reduction Anomaly The Dimensional-Reduction Anomaly

1999-09-13

arxiv.org/abs/hep-th/9909086v3

Phys.Rev. D61 (2000) 024021

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 28 pages, references added. To be published in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.61.024021

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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