Green-Schwarz superstring action in a curved magnetic Ramond-Ramond background

TL;DR

This paper derives the complete covariant superstring action in a curved D=10 background with magnetic Ramond-Ramond flux, obtained via dimensional reduction from a flat D=11 supermembrane, revealing a quadratic and quartic fermion structure.

Contribution

It provides the explicit covariant form of the superstring action in a non-trivial curved background with Ramond-Ramond flux, extending previous flat space formulations.

Findings

Derived the superstring action in a magnetic Ramond-Ramond background.

Connected the background to a dimensional reduction from D=11 supermembrane.

Presented the light-cone gauge action with quadratic and quartic fermion terms.

Abstract

We derive the complete covariant action for the type IIA superstring in a simple D=10 background which represents a 7-brane with a magnetic Ramond-Ramond vector field (and is U-dual to the Kaluza-Klein Melvin solution). This curved background can be obtained by dimensional reduction from a flat (but topologically non-trivial) D=11 space-time. The action of a supermembrane propagating in this flat D=11 space is straightforward to write down. The explicit form of the superstring action is then obtained by double dimensional reduction of the supermembrane action. In the light-cone gauge the action contains only quadratic and quartic terms in fermions.