Uniqueness Criteria for the Virasoro-Shapiro Amplitude

TL;DR

This paper establishes criteria for the uniqueness of the Virasoro-Shapiro amplitude by analytically bootstrapping the spectrum and four-point functions of closed string theory, revealing connections to extremal amplitudes and positivity.

Contribution

It introduces a novel bootstrap approach for closed string amplitudes based on high-energy falloff and level truncation, extending principles from open string theory.

Findings

Deformations maintain Regge scaling similar to gravity

In tensionless limit, reproduce extremal positivity amplitudes

Provides a parameterized space of consistent closed string amplitudes

Abstract

The scattering amplitudes of string theory exhibit many extraordinary properties. But are they the unique mathematical objects to do so? Recently, it has been shown how the spectrum and amplitudes of open string theory follow directly from the assumptions of faster than power-law falloff at high energies and a property dubbed level truncation. At present there is no analogous principle for closed string scattering, which is famously rigid and naively impervious to modification. In this paper we analytically bootstrap the spectrum and four-point amplitudes of the closed string -- together with a parameterized space of deformations -- from conditions on high-energy falloff and level truncation. While these deformations exhibit the same Regge scaling as pure gravity, in the tensionless limit they reproduce remarkable extremal amplitudes that have appeared in bottom-up studies of positivity.