The Dimensional reduction anomaly
Sep, 199928 pages
Published in:
- Phys.Rev.D 61 (2000) 024021
e-Print:
- hep-th/9909086 [hep-th]
Report number:
- ALBERTA-THY-15-99
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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.- space-time
- any-dimensional
- effective action
- dimensional reduction
- anomaly
- correlation function
- heat kernel
- analytic properties
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