Vertex Operators and Scattering Amplitudes of the Bosonic Open String Theory in the Linear Dilaton Background

TL;DR

This paper develops the operator formalism for bosonic open strings in a linear dilaton background, deriving vertex operators and computing scattering amplitudes, confirming Ward identities and conformal algebra consistency.

Contribution

It introduces explicit vertex operators and calculates tree-level scattering amplitudes in a linear dilaton background, extending string theory formalism.

Findings

Vertex operators satisfy the conformal algebra.

Tree-level amplitudes obey on-shell Ward identities.

Decoupling of zero-norm states is confirmed.

Abstract

The operator formalism of the first quantized string theory is applied to the stringy excitations in the linear dilaton background. In particular, the normal-ordered vertex operators in the old-covariant spectrum of the bosonic open string, which correspond to the physical state solutions of the Virasoro constraints, are shown to satisfy the conformal algebra. Tree-level scattering amplitudes among different stringy states are computed using the coherent-state method and the modified inner product of the Hilbert space. Decoupling of the zero-norm states, i.e., the on-shell stringy Ward identities are shown to hold for all tree-level amplitudes under consideration.