GREEN-SCHWARZ SUPERSTRING ACTION IN A CURVED MAGNETIC RAMOND-RAMOND BACKGROUND

We derive the complete covariant action for the type IIA superstring i n a simple D = 10 background which represents a 7-brane with a magneti c Ramond-Ramond vector field (and is U-dual to the Kaluza-Klein Melvin solution). This curved background can be obtained by dimensional redu ction from a at (but topologically non-trivial) D = 11 space-time. The action of a supermembrane propagating in this at D = 11 space is stra ightforward 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 an d quartic terms in fermions.