Marginal deformations of N=4 SYMN=4 SYM and open vs. closed string parameters

We make precise the connection between the generic Leigh–Strassler deformation of N=4 SYMN=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 corresponding deformed flat space geometry up to third order in the deformation parameter ρ.