High-energy zero-norm states and symmetries of string theory

TL;DR

This paper investigates high-energy zero-norm states in 26D open bosonic string theory to derive algebraic relations among scattering amplitudes, confirming Gross's conjecture and providing explicit amplitude calculations.

Contribution

It introduces a method to derive linear relations among high-energy string scattering amplitudes using zero-norm states, confirming and extending previous conjectures.

Findings

Ratios among high-energy scattering amplitudes are derived algebraically.

Leading order amplitudes are expressed in terms of four tachyon amplitudes.

Explicit calculations of amplitudes with three tachyons and one massive state confirm the theoretical results.

Abstract

High-energy limit of zero-norm states (HZNS) in the old covariant first quantized (OCFQ) spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed angle behavior of four point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, as a consistent sample calculation, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to justify our results.