The Veneziano Amplitude in any Dimension and a Virasoro-Shapiro Partial Amplitude

TL;DR

This paper generalizes the Veneziano amplitude to higher-dimensional world-surfaces, decomposes the Virasoro-Shapiro amplitude into partial amplitudes, and introduces a bootstrap principle to explore tachyon-free, supersymmetric variants.

Contribution

It extends the Veneziano amplitude to any dimension and proposes a new bootstrap method for tachyon-free, supersymmetric string amplitudes.

Findings

Decomposition of Virasoro-Shapiro amplitude into three partial amplitudes.

Generalization of Veneziano amplitude to higher-dimensional surfaces.

Introduction of a bootstrap principle for tachyon-free, supersymmetric amplitudes.

Abstract

This paper demonstrates how the Veneziano partial amplitude of bosonic string theory admits a generalization to world-(hyper)surfaces of any dimension $d$. In particular, for $d=2$, by carving up the worldsheet integral according to stipulations imposed on conformal cross ratios, the Virasoro-Shapiro full amplitude can be decomposed into a sum of three partial amplitudes. The amplitudes obtained on generalizing the Veneziano amplitude all contain tachyons. To explore candidate tachyon-free and supersymmetric versions of these amplitudes, a new bootstrap principle is introduced and applied, which demands that towers of residues alternate between all-even and all-odd spin partial waves.