Anatomy of Zero-norm States in String Theory

TL;DR

This paper explores the structure of zero-norm states across different string theory quantization schemes, revealing their role in gauge symmetries and high-energy scattering behaviors, thus deepening understanding of string symmetries.

Contribution

It systematically compares zero-norm states in covariant, light-cone, and BRST quantizations, linking gauge transformations in Witten string field theory to high-energy string symmetries.

Findings

Identified zero-norm states in multiple quantization schemes.

Linked off-shell gauge transformations to on-shell stringy gauge symmetries.

Connected zero-norm states to high-energy scattering amplitude relations.

Abstract

We calculate and identify the counterparts of zero-norm states in the old covariant first quantised (OCFQ) spectrum of open bosonic string in two other quantization schemes of string theory, namely the light-cone DDF zero-norm states and the off-shell BRST zero-norm states (with ghost) in the Witten string field theory (WSFT). In particular, special attention is paid to the inter-particle zero-norm states in all quantization schemes. For the case of the off-shell BRST zero-norm states, we impose the no ghost conditions and recover exactly two types of on-shell zero-norm states in the OCFQ string spectrum for the first few low-lying mass levels. We then show that off-shell gauge transformations of WSFT are identical to the on-shell stringy gauge symmetries generated by two types of zero-norm states in the generalized massive sigma-model approach of string theory. The high energy limit of these stringy gauge symmetries was recently used to calculate the proportionality constants, conjectured by Gross, among high energy scattering amplitudes of different string states. Based on these zero-norm state calculations, we have thus related gauge symmetry of WSFT to the high-energy stringy symmetry of Gross.