Sharp Boundaries for the Swampland

TL;DR

This paper establishes precise bounds on higher derivative couplings in weakly coupled gravitational theories using dispersive sum rules, analyticity, and Regge growth assumptions, with applications to scalar and supersymmetric models.

Contribution

It introduces a novel dispersive sum rule approach at small impact parameter to bound higher derivative couplings in gravity, overcoming previous challenges posed by the graviton pole.

Findings

Higher derivative couplings are bounded to be of order one in the UV cutoff units.

The method applies to theories with massless scalars and maximal supersymmetry.

The approach justifies the expectation of order-one couplings in consistent theories.

Abstract

We reconsider the problem of bounding higher derivative couplings in consistent weakly coupled gravitational theories, starting from general assumptions about analyticity and Regge growth of the S-matrix. Higher derivative couplings are expected to be of order one in the units of the UV cutoff. Our approach justifies this expectation and allows to prove precise bounds on the order one coefficients. Our main tool are dispersive sum rules for the S-matrix. We overcome the difficulties presented by the graviton pole by measuring couplings at small impact parameter, rather than in the forward limit. We illustrate the method in theories containing a massless scalar coupled to gravity, and in theories with maximal supersymmetry.