Dispersion Relations in String Theory

TL;DR

This paper derives dispersion relations for string scattering amplitudes, analyzing their analytic structure and decay rates, and compares string effects with field theory box diagrams, highlighting convergence issues.

Contribution

It provides explicit dispersion relations and decay formulas for string scattering amplitudes, connecting string theory effects with field theory analogs.

Findings

Explicit double and single dispersion relations derived.

Formulas for branch cuts and decay rates obtained.

String effects linked to convergence problems in superpositions.

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 $\phi^3$-like field theories. The stringy effects are traced to a convergence problem in this superposition.