Generalized On-Shell Ward Identities in String Theory

TL;DR

The paper constructs an infinite set of on-shell Ward identities in string theory at tree level, valid to all loop orders, using zero-norm states, and demonstrates their implications for scattering amplitudes and gauge symmetries.

Contribution

It introduces a systematic method to derive on-shell Ward identities in string theory without string field theory, extending understanding of gauge symmetries at all loop levels.

Findings

Explicit calculation of bosonic massive scattering amplitudes up to second excited states.

Derivation of Ward identities using zero-norm states in the spectrum.

Identification of a large gauge multiplet structure at the second massive level.

Abstract

It is demonstrated that an infinite set of string-tree level on-shell Ward identities, which are valid to all sigma-model loop orders, can be systematically constructed without referring to the string field theory. As examples, bosonic massive scattering amplitudes are calculated explicitly up to the second massive excited states. Ward identities satisfied by these amplitudees are derived by using zero-norm states in the spetrum. In particular, the inter-particle Ward identity generated by the D2xD2' zero-norm state at the second massive level is demonstrated. The four physical propagating states of this mass level are then shown to form a large gauge multiplet. This result justifies our previous consideration on higher inter-spin symmetry from the generalized worldsheet sigma-model point of view.