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

TL;DR

This paper explores supergravity solutions with self-dual B fields and their relation to noncommutative Yang-Mills theory, demonstrating that certain geometries and instanton actions remain consistent in the decoupling limit.

Contribution

It constructs D-instanton solutions in supergravity with self-dual B fields and shows their actions match noncommutative Yang-Mills instantons, revealing new aspects of the duality.

Findings

The Einstein frame metric remains unchanged with B fields in the decoupling limit.

D-instanton actions in supergravity match those in noncommutative Yang-Mills theory.

The geometry is asymptotically flat, affecting the duality features.

Abstract

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.