Bootstrapping Gravity with Crossing Symmetric Dispersion Relations

TL;DR

This paper develops crossing symmetric dispersion relations to derive bounds on gravitational Wilson coefficients, providing a new, more powerful method for constraining low-energy effective theories of gravity.

Contribution

It introduces crossing symmetric sum rules that isolate low-energy couplings without forward limit assumptions, improving bounds on gravitational interactions.

Findings

Stronger bounds on graviton scattering amplitudes.

Validation against previous scalar and supergraviton bounds.

New bounds on graviton coupling to massive spin-4 states.

Abstract

We derive bounds on Wilson coefficients in gravitational effective field theories using fully crossing symmetric dispersion relations. These sum rules naturally isolate finite subsets of low-energy couplings without relying on the forward limit or specific high-energy completions. We validate our method by matching bounds computed previously for scalar scattering with gravity as well as for supergraviton scattering. For graviton scattering we use crossing symmetric functions that combine various helicity combinations for the maximal-helicity violating amplitude and find stronger bounds than have been previously computed. We also derive new bounds on the coupling of gravitons to a massive spin-4 state at tree level. These results demonstrate the power of crossing symmetric sum rules as a tool in the S-matrix bootstrap.