Veneziano Variations: How Unique are String Amplitudes?

TL;DR

This paper introduces a new family of four-point string scattering amplitudes with adjustable parameters, generalizing known amplitudes like Veneziano and Coon, and explores their properties, spectra, and unitarity conditions.

Contribution

It derives a multi-parameter class of amplitudes with customizable Regge trajectories, unbounded or bounded spectra, and analyzes their unitarity and high-energy behavior.

Findings

Amplitudes exhibit polynomially bounded high-energy behavior.

Mass spectra can be unbounded or bounded with accumulation points.

Identifies unitary regions in parameter space for these amplitudes.

Abstract

String theory offers an elegant and concrete realization of how to consistently couple states of arbitrarily high spin. But how unique is this construction? In this paper we derive a novel, multi-parameter family of four-point scattering amplitudes exhibiting i) polynomially bounded high-energy behavior and ii) exchange of an infinite tower of high-spin modes, albeit with a finite number of states at each resonance. These amplitudes take an infinite-product form and, depending on parameters, exhibit mass spectra that are either unbounded or bounded, thus corresponding to generalizations of the Veneziano and Coon amplitudes, respectively. For the bounded case, masses converge to an accumulation point, a peculiar feature seen in the Coon amplitude but more recently understood to arise naturally in string theory. Importantly, our amplitudes contain free parameters allowing for the customization of the slope and offset of the spin-dependence in the Regge trajectory. We compute all partial waves for this multi-parameter class of amplitudes and identify unitary regions of parameter space. For the unbounded case, we apply similar methods to derive new deformations of the Veneziano and Virasoro-Shapiro amplitudes.