  We derive two sum rules by studying the low energy Compton scattering on a
target of arbitrary (nonzero) spin j. In the first sum rule, we consider the
possibility that the intermediate state in the scattering can have spin |j \pm
1| and the same mass as the target. The second sum rule applies if the theory
at hand possesses intermediate narrow resonances with masses different from the
mass of the scatterer. These sum rules are generalizations of the
Gerasimov-Drell-Hearn-Weinberg sum rule. Along with the requirement of tree
level unitarity, they relate different low energy couplings in the theory.
Using these sum rules, we show that in certain cases the gyromagnetic ratio can
differ from the "natural" value g=2, even at tree level, without spoiling
perturbative unitarity. These sum rules can be used as constraints applicable
to all supergravity and higher-spin theories that contain particles charged
under some U(1) gauge field. In particular, applied to four dimensional N=8
supergravity in a spontaneously broken phase, these sum rules suggest that for
the theory to have a good ultraviolet behavior, additional massive states need
to be present, such as those coming from the embedding of the N=8 supergravity
in type II superstring theory. We also discuss the possible implications of the
sum rules for QCD in the large-N_c limit.
