Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude

TL;DR

This paper demonstrates that theories with massive higher-spin particles, including string theory and Yang-Mills, exhibit a universal amplitude in high-energy regimes, aligning with the Veneziano amplitude and implying string-like features.

Contribution

It proves that theories with higher-spin particles necessarily have string-like excitations and asymptotically linear Regge trajectories, establishing a universality of the Veneziano amplitude in certain regimes.

Findings

Amplitude coincides with Veneziano amplitude at high energies.

Leading Regge trajectory is asymptotically linear in Yang-Mills.

Presence of stringy excitations and infinite subleading trajectories.

Abstract

We consider weakly-coupled theories of massive higher-spin particles. This class of models includes, for instance, tree-level String Theory and Large-N Yang-Mills theory. The S-matrix in such theories is a meromorphic function obeying unitarity and crossing symmetry. We discuss the (unphysical) regime $s,t \gg 1$, in which we expect the amplitude to be universal and exponentially large. We develop methods to study this regime and show that the amplitude necessarily coincides with the Veneziano amplitude there. In particular, this implies that the leading Regge trajectory, $j(t)$, is asymptotically linear in Yang-Mills theory. Further, our analysis shows that any such theory of higher-spin particles has stringy excitations and infinitely many asymptotically parallel subleading trajectories. More generally, we argue that, under some assumptions, any theory with at least one higher-spin particle must have strings.