Bootstrap Principle for the Spectrum and Scattering of Strings

TL;DR

This paper demonstrates that the Veneziano amplitude is uniquely determined by a bootstrap approach based on high-energy behavior and cancellation conditions, deriving the string spectrum and scattering amplitude.

Contribution

It introduces a bootstrap framework that uniquely recovers the Veneziano amplitude and spectrum from analyticity and high-energy assumptions, extending to a family of solutions.

Findings

Veneziano amplitude is the unique solution under specified assumptions.

The bootstrap approach recovers the string spectrum and scattering amplitude.

A family of solutions includes known amplitudes like Coon and hypergeometric.

Abstract

We show that the Veneziano amplitude of string theory is the unique solution to an analytically solvable bootstrap problem. Uniqueness follows from two assumptions: faster than power-law falloff in high-energy scattering and the existence of some infinite sequence in momentum transfer at which higher-spin exchanges cancel. The string amplitude-including the mass spectrum-is an output of this bootstrap. If the amplitude merely vanishes at high energies, the solution is a three-parameter family containing the Veneziano, Coon, and hypergeometric amplitudes, and more.