D1/D5 system with B-field, noncommutative geometry and the CFT of the Higgs branch

Abstract

The D1/D5 system is considered in the presence of the NS B field. An explicit supergravity solution in the asymptotically flat and near horizon limits is presented. Explicit mass formulae are presented in both cases. This solution has no D3 source branes and represents a true bound state of the D1/D5 system. We study the motion of a separated D1-brane in the background geometry described above and reproduce the Liouville potential that binds the D1 brane. A gauge theory analysis is also presented in the presence of Fayet-Iliopoulos (FI) parameters which can be identified with the self-dual part of the NS B field. In the case of a single D5-brane and an arbitrary number of D1-branes we can demonstrate the existence of a bound state in the Higgs branch. We also point out the connection of the SCFT on the resolved Sym _Q1Q5(T˜⁴) with recent developments in non-commutative Yang-Mills theory.