Where is tree-level string theory?

TL;DR

This paper explores the landscape of consistent tree-level supergravity extensions, identifying a string-like extremal solution with a Regge trajectory and revealing a continuous family of solutions with varying slopes.

Contribution

It introduces a bootstrap approach to constrain supergravity extensions and uncovers a novel extremal solution resembling string theory, along with a family of solutions with different Regge slopes.

Findings

Type II string theory is within the allowed parameter space.

A new extremal solution with a single Regge trajectory was found.

A continuous family of solutions with varying Regge slopes was identified.

Abstract

We investigate the space of consistent tree-level extensions of the maximal supergravities in ten dimensions. We parametrize theory space by the first few EFT coefficients and by the on-shell coupling of the lightest massive state, and impose on these data the constraints that follow from $2 \to 2$ supergraviton scattering. While Type II string theory lives strictly inside the allowed region, we uncover a novel extremal solution of the bootstrap problem, which appears to contain a single linear Regge trajectory, with the same slope as string theory. We repeat a similar analysis for supergluon scattering, where we find instead a continuous family of extremal solutionswith a single Regge trajectory of varying slope.