DISPERSION-RELATIONS IN STRING THEORY

We analyze the analytic continuation of the formally divergent one-loo p amplitude for scattering of the graviton multiplet in the Type II su perstring. In particular we obtain explicit double and single dispersi on relations, formulas for all the successive branch cuts extending ou t to +infinity, as well as for the decay rate of a massive string stat e of arbitrary mass 2N into two string states of lower mass. We compar e our results with the box diagram in a superposition of phi(3)-like f ield theories. The stringy effects are traced to a convergence problem in this superposition.