Anatomy of zero-norm states in string theory

Abstract

We calculate and identify the counterparts of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string in two other quantization schemes of string theory, namely, the light-cone Del Giudice--Di Vecchia--Fubine zero-norm states and the off-shell Becchi-Rouet-Stora-Tyutin (BRST) zero-norm states (with ghost) in the Witten string field theory (WSFT). In particular, special attention is paid to the interparticle 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 $\ensuremath{\sigma}$-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.