Quantization of the Type II Superstring in a Curved Six-Dimensional Background

TL;DR

This paper constructs a sigma model for the Type II superstring in a six-dimensional curved background with flux, enabling quantization and connecting to known models in specific geometries.

Contribution

It develops a linear sigma model action for the superstring in curved six-dimensional backgrounds with Ramond-Ramond flux, extending previous flat-space formulations.

Findings

The sigma model is quantizable in flat spacetime.

The model reduces to known actions in $AdS_3\times S^3$ backgrounds.

Provides a framework for studying superstrings in curved flux backgrounds.

Abstract

A sigma model action with N=2 D=6 superspace variables is constructed for the Type II superstring compactified to six curved dimensions with Ramond-Ramond flux. The action can be quantized since the sigma model is linear when the six-dimensional spacetime is flat. When the six-dimensional spacetime is $AdS_3\times S^3$, the action reduces to one found earlier with Vafa and Witten.