Abstract
In a wide class of D-dimensional spacetimes which are direct or semi-direct sums of a -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 -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 -dimensional effective actions, this property is violated after renormalization. We calculate the corresponding anomalous terms explicitly, illustrating the effect with some simple examples.
- Received 22 September 1999
DOI:https://doi.org/10.1103/PhysRevD.61.024021
©1999 American Physical Society