Where is String Theory?

TL;DR

This paper uses the S-matrix bootstrap to explore the space of graviton scattering amplitudes in ten dimensions, revealing how string theory spans a wide range of the allowed parameter space from weak to strong coupling.

Contribution

It applies the S-matrix bootstrap to identify allowed and excluded regions of Wilson coefficients in ten-dimensional supergravity, connecting these findings to string theory.

Findings

Negative Wilson coefficient region is excluded by unitarity.

Allowed region extends from large positive to the swamp boundary.

String theory covers nearly the entire allowed parameter space.

Abstract

We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading Wilson coefficient $\alpha$ controlling the leading correction to maximal supergravity. The negative region $\alpha<0$ is excluded by a simple dual argument based on linearized unitarity (the desert). A whole semi-infinite region $\alpha \gtrsim 0.14$ is allowed by the primal bootstrap (the garden). A finite intermediate region is excluded by non-perturbative unitarity (the swamp). Remarkably, string theory seems to cover all (or at least almost all) the garden from very large positive $\alpha$ -- at weak coupling -- to the swamp boundary -- at strong coupling.