Decoupling of Degenerate Positive-norm States in Witten's String Field Theory

TL;DR

This paper demonstrates that in Witten's string field theory, degenerate positive-norm states can be gauged to higher rank fields, simplifying scattering amplitude calculations and linking zero-norm states with background ghost fields.

Contribution

It reveals a gauge equivalence between degenerate positive-norm states and higher rank fields in WSFT, supported by explicit calculations up to the fifth spin level.

Findings

Degenerate positive-norm states can be gauged to higher rank fields.

Scattering amplitudes of these states relate to those of higher spin fields.

Zero-norm states correspond to background ghost fields in off-shell gauge transformations.

Abstract

We show that the degenerate positive-norm physical propagating fields of the open bosonic string can be gauged to the higher rank fields at the same mass level. As a result, their scattering amplitudes can be determined from those of the higher spin fields. This phenomenon arises from the existence of two types of zero-norm states with the same Young representations as those of the degenerate positive-norm states in the old covariant first quantized (OCFQ) spectrum. This is demonstrated by using the lowest order gauge transformation of Witten's string field theory (WSFT) up to the fourth massive level (spin-five), and is found to be consistent with conformal field theory calculation based on the first quantized generalized sigma-model approach. In particular, on-shell conditions of zero-norm states in OCFQ stringy gauge transformation are found to correspond, in a one-to-one manner, to the background ghost fields in off-shell gauge transformation of WSFT. The implication of decoupling of scalar modes on Sen's conjectures was also briefly discussed.