# General fluctuations of the heterotic pure spinor string on curved backgrounds

## TL;DR

This paper investigates the structure of vertex operators for heterotic superstrings in the pure spinor formalism, extending from flat to curved backgrounds, highlighting the role of reparametrization ghosts in their construction.

## Contribution

It provides a detailed analysis of fluctuations and vertex operators for heterotic superstrings on curved backgrounds within the pure spinor framework, emphasizing the role of reparametrization ghosts.

## Key findings

- Vertex operators for curved backgrounds are constructed.
- Reparametrization ghosts are crucial in vertex operator formulation.
- The formalism extends flat background results to curved geometries.

## Abstract

The general fluctuations, in the form of vertex operators, for the heterotic superstring in the pure spinor formalism are considered. The case of a flat background is reviewed and the case of a curved case is studied. The left-moving ghosts are pure spinors and the right-moving ghosts come from fixing the reparametrization invariance. The role of the reparametrization ghosts in the construction of the vertex operators is emphasized.