Eikonal resummation and topological expansion coefficients in superstring theory

We explicitly show that in the Regge regime of large s, fixed t the leading part of the g-loop amplitude for the scattering of two gravitons is the product of g+1 tree amplitudes times the expectation value of a factorized operator. This result proves that the superstring loop series is summable in the eikonal approximation. We determine the normalization dictated by unitarity of all terms in the topological expansion as a function of the two independent constants in the theory, the string tension 1/α' and the coupling constant g. (orig.)