Multiparticle Factorization and the Rigidity of String Theory

TL;DR

This paper investigates the uniqueness of string theory by analyzing higher-point scattering factorization constraints, which strongly restrict possible deformations and allow direct extraction of three-point amplitudes for string modes.

Contribution

It introduces a systematic method to constrain string deformations using higher-point factorization, excluding several proposed modifications and deriving three-point amplitudes without vertex operators.

Findings

Certain proposed string deformations are excluded by factorization constraints.

The formalism enables direct extraction of three-point string amplitudes.

String theory remains consistent under the analyzed constraints.

Abstract

Is string theory uniquely determined by self-consistency? Causality and unitarity seemingly permit a multitude of putative deformations, at least at the level of two-to-two scattering. Motivated by this question, we initiate a systematic exploration of the constraints on scattering from higher-point factorization, which imposes extraordinarily restrictive sum rules on the residues and spectra defined by a given amplitude. These bounds handily exclude several proposed deformations of the string: the simplest "bespoke" amplitudes with tunable masses and a family of modified string integrands from "binary geometry." While the string itself passes all tests, our formalism directly extracts the three-point amplitudes for the low-lying string modes without the aid of worldsheet vertex operators.