Marginal Deformations of N=4 SYM and Open vs. Closed String Parameters

Abstract

We make precise the connection between the generic Leigh--Strassler deformation of N=4 SYM and noncommutativity. We construct an appropriate noncommutativity matrix, which turns out to define a nonassociative deformation. Viewing this noncommutativity matrix as part of the set of open string data which characterize the deformation and mapping them to the closed string data (e.g. metric and B--field), we are able to construct the gravity dual and the the correponding deformed flat space geometry up to third order in the deformation parameter.