String coherent vertex operators of Neveu-Schwarz and Ramond states

TL;DR

This paper develops explicit, supersymmetry-compatible coherent vertex operators for Neveu-Schwarz and Ramond states in superstring theory, enabling simplified amplitude calculations and extending to type IIA and IIB superstrings.

Contribution

It provides a compact, manifestly BRST-invariant construction of coherent vertex operators for both Neveu-Schwarz and Ramond sectors, including explicit forms and amplitude computations.

Findings

Constructed explicit coherent vertex operators for NS and R sectors.

Demonstrated BRST invariance and covariance of the operators.

Computed tree-level three-point scattering amplitudes.

Abstract

We present a compact expression for a coherent vertex operator in superstring theory, in the Neveu-Schwarz sector, that can be easily extended to the Ramond sector by supersymmetric transformations in target space. We give also an explicit construction for the Ramond coherent vertex operator. These constructions provide the use of the supersymmetric version of the Del Giudice-Di Vecchia-Fubini operators and Operator Product Expansion techniques, displaying manifest BRST invariance and after normal ordering also manifest covariance. As a consistency check we compute tree level three-points scattering amplitudes involving Neveu-Schwarz coherent vertex operators in different superghost pictures. Extending these results to the closed superstring, we give the expressions of the coherent vertex operators in the case of type IIA and IIB theories.