# General fluctuations of the type II pure spinor string on curved backgrounds

## TL;DR

This paper reviews the construction of vertex operators for type II superstrings in the pure spinor formalism, extending from flat space to generic curved supergravity backgrounds, highlighting the formalism's applicability in complex backgrounds.

## Contribution

It introduces a systematic method to construct vertex operators for type II superstrings in arbitrary curved supergravity backgrounds within the pure spinor formalism.

## Key findings

- Vertex operators constructed for curved backgrounds
- Extension of flat space formalism to generic supergravity backgrounds
- Framework facilitates calculations in complex string backgrounds

## Abstract

The general fluctuations, in the form of vertex operators, for the type II superstring in the pure spinor formalism are considered. We review the construction of these vertex operators in flat space-time. We then review the type II superstrings in curved background in the pure spinor formalism to finally construct the vertex operators on a generic type II supergravity background.