Gravitons and the Drell–Hearn–Gerasimov sum rule

One-loop diagrams containing a graviton provide a finite contribution to the anomalous magnetic moment aℓ of a lepton, whether or not the graviton propagates in n large extra compact dimensions. In the present work, the tree graph photoproduction of a graviton, integrated up to an arbitrary cutoff, is shown to violate the Drell–Hearn–Gerasimov sum rule for aℓ2. The possibility of resurrecting the sum rule from high energy contributions originating in string excitations is discussed in a qualitative manner, and various problems associated with such a program are pointed out.