  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.
