Dispersion Relations in String Theory

Abstract

We analyze the analytic continuation of the formally divergent one-loop amplitude for scattering of the graviton multiplet in the Type II Superstring. In particular we obtain explicit double and single dispersion relations, formulas for all the successive branch cuts extending out to plus infinity, as well as for the decay rate of a massive string state of arbitrary mass 2N into two string states of lower mass. We compare our results with the box diagram in a superposition of $φ^3$-like field theories. The stringy effects are traced to a convergence problem in this superposition.