Supergravity Duals of Noncommutative Wrapped D6 Branes and Supersymmetry without Supersymmetry

TL;DR

This paper constructs an 11-dimensional supergravity solution describing wrapped D6-branes with a B-field, revealing a natural occurrence of supersymmetry without actual supersymmetry in certain compactifications.

Contribution

It presents a novel 11d supergravity background for wrapped D6-branes with noncommutativity, highlighting supersymmetry phenomena not captured by 8d gauged supergravity.

Findings

Constructed a supergravity solution with D6-branes and B-field.

Identified supersymmetry without supersymmetry in compactifications.

Provided an 11d background with four supercharges and flux.

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.