Symmetries of the Bosonic String S-Matrix

TL;DR

This paper derives a set of finite difference relations for the bosonic string S-matrix using BRST classes, Lorentz invariance, and analyticity, which uniquely determine the genus zero scattering amplitudes for up to 26 particles in 25+1 dimensions.

Contribution

It introduces a novel approach combining BRST classes, Lorentz invariance, and analyticity to determine the string S-matrix uniquely from physical criteria.

Findings

Finite difference relations determine the genus zero S-matrix.

Relations depend on a single parameter, the string coupling .

High-energy limits relate to string theory Ward identities.

Abstract

The bracket operation on mutually local BRST classes may be combined with Lorentz invariance and analyticity to write an infinite set of finite difference relations on string scattering amplitudes. When combined with some simple physical criteria these relations uniquely determine the genus zero string $S$-matrix for $N\leq 26$-particle scattering in $\IR^{25,1}$ in terms of a single parameter, $\kappa$, the string coupling. We propose that the high-energy limit of the relations are the Ward identities for the high-energy symmetries of string theory.