A stringy dispersion relation for field theory

TL;DR

This paper introduces a new local, crossing symmetric dispersion relation for 2-2 scattering amplitudes, inspired by string theory, with applications to bounding Wilson coefficients in gravitational effective field theories.

Contribution

It develops a parametric family of dispersion relations that unify known forms and provides new series representations for string amplitudes, facilitating bootstrap approaches.

Findings

Derived a parametric dispersion relation unifying fixed-t and fixed-s forms.

Presented series representations for Veneziano and Virasoro-Shapiro amplitudes with manifest poles.

Applied the formalism to bound Wilson coefficients in gravitational EFTs.

Abstract

We derive a local, crossing symmetric dispersion relation (CSDR) for 2-2 scattering amplitudes with a parametric ambiguity motivated by string theory. Various limits of the parameter lead to the fixed-t, fixed-s, and other known CSDRs. We also present formulae for higher-subtracted cases. Several examples are discussed for illustration. In particular, for the Veneziano and the Virasoro-Shapiro amplitudes, we derive parametric series representations which manifest poles in all channels and converge everywhere. We then discuss applications of our formalism for bootstrapping weakly-coupled gravitational EFTs. We demonstrate that even in the presence of the graviton pole, one can derive bounds on the Wilson coefficients while working in the forward limit, with the parameter acting as the IR regulator instead. Finally, we derive series representations for multi-variable, totally symmetric generalisations of the Veneziano and Virasoro-Shapiro amplitudes that manifest poles in all the variables. This is a first step towards dispersion relations for n-particle scattering amplitudes.