Supergravity Duals of Noncommutative Wrapped D6 Branes and Supersymmetry without Supersymmetry

Abstract

We construct the supergravity solution in 11 dimensions describing D6-branes wrapped around a Kahler four-cycle with a B-field along the flat directions of the brane. The configuration is dual to an N=2 noncommutative gauge theory in 2+1 dimensions. We also construct the four associated independent Killing spinors. The phenomenon of supersymmetry without supersymmetry appears naturally when compactifying to type IIA or 8d gauged supergravity. Therefore, this solution also provides an 11d background with four supercharges and four-form flux, which is not obtainable from 8d gauged supergravity.