Positivity of the Veneziano Amplitude in Ten Dimensions

TL;DR

This paper provides a direct proof of the positivity of the Veneziano amplitude in ten dimensions, confirming its consistency with unitarity and extending the understanding of string scattering amplitudes.

Contribution

It offers the first direct proof of the partial-wave positivity of the Veneziano amplitude in ten dimensions, expanding the scope of amplitude positivity results.

Findings

Proves positivity of the Veneziano amplitude in D≤10 dimensions.

Demonstrates the proof can be adapted for other amplitudes in the S-matrix bootstrap.

Confirms the unitarity of open superstring scattering in ten dimensions.

Abstract

The Veneziano amplitude describing the tree-level scattering of four open superstrings is expected to be consistent with unitarity in ten spacetime dimensions. While this follows indirectly from the no-ghost theorem, a direct proof at the level of the amplitude has only been found for $D\leq 6$. In this article, we close this gap by providing a complete proof for the partial-wave positivity of the Veneziano amplitude in $D\leq 10$, derived directly from its definition in terms of the Euler beta function. We also demonstrate that this proof can be modified to show positivity of a wider family of amplitudes relevant to the $S$-matrix bootstrap.