Stringy Symmetries and Their High-energy Limits

TL;DR

This paper derives all-energy, all-loop string symmetries from zero-norm states, enabling algebraic determination of scattering amplitude ratios and revealing new amplitude components crucial for gauge invariance.

Contribution

It introduces a method to derive string symmetries from zero-norm states, applicable at all energies and loop orders, and identifies new amplitude components essential for gauge invariance.

Findings

Stringy symmetries derived from zero-norm states

Proportionality constants between amplitudes are angle- and order-independent

Discovery of new high-energy amplitude components

Abstract

We derive stringy symmetries with conserved charges of arbitrarily high spins from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. These symmetries are valid to all energy and all loop orders in string perturbation theory. The high-energy limit of these stringy symmetries can then be used to fix the proportionality constants between scattering amplitudes of different string states algebraically without referring to Gross and Mende's saddle point calculation of high-energy string-loop amplitudes. These proportionality constants are, as conjectured by Gross, independent of the scattering angle and the order of string perturbation theory. However, we also discover some new nonzero components of high-energy amplitudes not found previously by Gross and Manes. These components are essential to preserve massive gauge invariances or decouple massive zero-norm states of string theory. A set of massive scattering amplitudes and their high energy limit are calculated explicitly to justify our results.