Ward Identities and High-energy Scattering Amplitudes in String Theory

TL;DR

This paper uses Ward identities from zero-norm states to verify and correct high-energy scattering amplitude calculations in string theory, demonstrating a universal formula relating all such amplitudes to tachyon interactions.

Contribution

It introduces a method to verify high-energy string scattering amplitudes using Ward identities and derives a universal formula relating all amplitudes to tachyon amplitudes.

Findings

Identified inconsistencies in previous saddle point calculations.

Corrected the calculations to satisfy stringy Ward identities.

Proved a universal formula expressing all high-energy amplitudes in terms of tachyon amplitudes.

Abstract

High-energy limit of stringy Ward identities derived from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string are used to check the consistency of saddle point calculations of high energy scattering amplitudes of Gross and Mende and Gross and Manes. Some inconsistencies of their saddle point calculations are found even for the string-tree scattering amplitudes of the excited string states. We discuss and calculate the missing terms of the calculation by those authors to recover the stringy Ward identities. In addition, based on the tree-level stringy Ward identities, we give the proof of a general formula, which was proposed previously, of all high energy four-point string-tree amplitudes of arbitrary particles in the string spectrum. In this formula all such scattering amplitudes are expressed in terms of those of tachyons as conjectured by Gross. The formula is extremely simple which manifestly demonstrates the universal high energy behavior of the interactions among all string states.