Vertex Operators for Closed Superstrings

TL;DR

This paper develops a method to compute vertex operators for closed superstrings in various backgrounds, including RR fields, and introduces new tools for string field theory and superspace deformations.

Contribution

It presents an iterative procedure for vertex operators in covariant formalism, extending to massive states and proposing a kinetic term for closed string field theory.

Findings

Constructed vertex operators for generic backgrounds with RR fields.

Identified two new nilpotent charges for gauge fixing.

Proposed a kinetic term for closed string field theory.

Abstract

We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any generic background in presence of Ramond-Ramond (RR) fields. We extend the procedure to all massive states of open and closed superstrings and we identify two new nilpotent charges which are used to impose the gauge fixing on the physical states. We solve iteratively the equations of the vertex for linear x-dependent RR field strengths. This vertex plays a role in studying non-constant C-deformations of superspace. Finally, we construct an action for the free massless sector of closed strings, and we propose a form for the kinetic term for closed string field theory in the pure spinor formalism.