Supergravity with Self-dual B fields and Instantons in Noncommutative Gauge Theory

We study Type IIB supergravity in the presence of (euclidean) D3 branes and nonzero self-dual B-fields. We point out that the Einstein frame metric is identical to the full geometry for D3 branes without B fields turned on. Furthermore, in a decoupling limit in which the theory is conjectured to be dual to noncommutative Yang-Mills theory, the entire Einstein metric remains intact, and in particular, is asymptotically flat. We construct D-instanton solutions in this geometry. We show that in the decoupling limit the D-instanton action agrees with the action of the corresponding instanton in the noncommutative Yang-Mills theory and is expressed in terms of the open string coupling. Some other aspects of this correspondence, which have unusual features because the underlying metric is asymptotically flat, are explored.