Hyper-Kahler manifolds and multiply-intersecting branes

TL;DR

This paper explores the dualities and intersections of branes in supergravity theories, revealing new solutions with specific supersymmetry preservation and mapping between different dimensional frameworks.

Contribution

It introduces new intersecting brane solutions in supergravity, demonstrating dualities and supersymmetry properties, including solutions with arbitrary angles and multiple branes.

Findings

New 3/16 supersymmetric IIB solutions from hyper-Kähler manifolds

Mapping of solutions between D=11 and IIB supergravity

Discovery of 1/8 supersymmetric intersecting brane solutions

Abstract

Generalized membrane solutions of D=11 supergravity, for which the transverse space is a toric hyper-K{\" a}hler manifold, are shown to have IIB duals representing the intersection of parallel 3-branes with 5-branes whose orientations are determined by their $Sl(2;\bZ)$ charge vectors. These IIB solutions, which generically preserve 3/16 of the supersymmetry, can be further mapped to solutions of D=11 supergravity representing the intersection of parallel membranes with any number of fivebranes at arbitrary angles. Alternatively, a subclass (corresponding to non-singular D=11 solutions) can be mapped to solutions representing the intersection on a string of any number of D-5-branes at arbitrary angles, again preserving 3/16 supersymmetry, as we verify in a special case by a quaternionic extension of the analysis of Berkooz, Douglas and Leigh. We also use similar methods to find new 1/8 supersymmetric solutions of orthogonally intersecting branes.