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 $\al^2$. 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.