Natural Generalization of Bosonic String Amplitudes

TL;DR

This paper introduces a generalized scalar amplitude $S^{n}$ inspired by string theory forms, exhibiting key properties like conformal symmetry and Regge trajectories, and discusses its factorization and critical dimension for consistency.

Contribution

It proposes a natural $S^{n}$ generalization of string amplitudes, extending their properties and analyzing conditions for quantum consistency.

Findings

$S^{n}$ shares conformal symmetry and Regge trajectories with string amplitudes.

The paper discusses factorization and critical dimension for unitarity.

The generalized amplitude maintains key features of string theory amplitudes.

Abstract

The similarity between tree-level string theory scalar amplitudes, the Koba-Nielsen form ($S^{1}$) and the Virasoro-Shapiro form ($S^{2}$) suggests a natural $S^{n}$ generalization for a scalar amplitude. It is shown that the $S^{n}$ amplitude shares many essential properties of the string theory amplitudes, including $SO(n+1,1)$ conformal symmetry and linear Regge trajectories for the mass spectrum. We also discuss factorization and the critical dimension for the amplitude, which are the necessary conditions for the quantum mechanical consistency (unitarity) of the amplitude.