In theories with chiral couplings, one of the important consistency
requirements is that of the cancellation of a gauge anomaly. In particular,
this is one of the conditions imposed on the hypercharges in the Standard
Model. However, anomaly cancellation condition of the Standard Model looks
unnatural from the perspective of a theory with extra dimensions. Indeed, if
our world were embedded into an odd-dimensional space, then the full theory
would be automatically anomaly free. In this paper we discuss the physical
consequences of anomaly non-cancellation for effective 4-dimensional field
theory. We demonstrate that in such a theory parallel electric and magnetic
fields get modified. In particular, this happens for any particle possessing
both electric charge and magnetic moment. This effect, if observed, can serve
as a low energy signature of extra dimensions. On the other hand, if such an
effect is absent or is very small, then from the point of view of any theory
with extra dimensions it is just another fine-tuning and should acquire
theoretical explanation.Comment: 23 pages plus appendices, 3 figures. v2: final journal version.
References added; corrections to Appendix
