Corners and Islands in the S-matrix Bootstrap of the Open Superstring

TL;DR

This paper uses bootstrap methods to analyze the open superstring amplitude, revealing sharp bounds and specific spectral properties consistent with string theory, and compares these results with other bootstrap approaches.

Contribution

It introduces a bootstrap framework for the Veneziano superstring amplitude, identifying unique bounds and spectral constraints that match string theory predictions.

Findings

Veneziano amplitude located at a sharp corner in parameter space.

A one-parameter family of EFT bounds corresponding to Regge trajectories.

The second massive state's properties are determined by the bootstrap when fixing certain couplings.

Abstract

We bootstrap the Veneziano superstring amplitude in 10 dimensions from the bottom-up. Starting with the most general maximally supersymmetric Yang-Mills EFT, we input information about the lowest-lying massive states, which we assume contribute via tree-level exchanges to the 4-point amplitude. We show the following: (1) if there is only a single state at the lowest mass, it must be a scalar. (2) Assuming a string-inspired gap between the mass of this scalar and any other massive states, the allowed region of Wilson coefficients has a new sharp corner where the Veneziano amplitude is located. (3) Upon fixing the next massive state to be a vector, the EFT bounds have a one-parameter family of corners; these would correspond to models with linear Regge trajectories of varying slopes, one of which is the open superstring. (4) When the ratio between the massive scalar coupling and the $\text{tr}\, F^4$ coefficient is fixed to its string value, the spin and mass of the second massive state is determined by the bootstrap and the Veneziano amplitude is isolated on a small island in parameter space. Finally, we compare with other recent bootstraps approaches, both the pion model and imposing Regge-inspired maximal spin constraints.