Dimensional-reduction anomaly - art. no. 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 "intern al" space, a field can be decomposed into modes. As a result of this mode d ecomposition, the main objects which characterize the free quantum field, s uch as Green functions and heat kernels, can effectively be reduced to obje cts in a (D-n)-dimensional spacetime with an external dilaton field. We stu dy the problem of the dimensional reduction of the effective action for suc h spacetimes. While before renormalization the original D-dimensional effec tive action can be presented as a "sum over modes'' of (D-n)-dimensional ef fective actions, this property is violated after renormalization. We calcul ate the corresponding anomalous terms explicitly, illustrating the effect w ith some simple examples.