Flows on quaternionic-Kaehler and very special real manifolds

Details Flows on quaternionic-Kaehler and very special real manifolds Flows on quaternionic-Kaehler and very special real manifolds

2001-09-12

arxiv.org/abs/hep-th/0109094v1

Commun.Math.Phys. 238 (2003) 525-543

Physics

High Energy Physics

High Energy Physics - Theory

22 pages

Scientific paper

10.1007/s00220-003-0850-4

BPS solutions of 5-dimensional supergravity correspond to certain gradient flows on the product M x N of a quaternionic-Kaehler manifold M of negative scalar curvature and a very special real manifold N of dimension n >=0. Such gradient flows are generated by the `energy function' f = P^2, where P is a (bundle-valued) moment map associated to n+1 Killing vector fields on M. We calculate the Hessian of f at critical points and derive some properties of its spectrum for general quaternionic-Kaehler manifolds. For the homogeneous quaternionic-Kaehler manifolds we prove more specific results depending on the structure of the isotropy group. For example, we show that there always exists a Killing vector field vanishing at a point p in M such that the Hessian of f at p has split signature. This generalizes results obtained recently for the complex hyperbolic plane (universal hypermultiplet) in the context of 5-dimensional supergravity. For symmetric quaternionic-Kaehler manifolds we show the existence of non-degenerate local extrema of f, for appropriate Killing vector fields. On the other hand, for the non-symmetric homogeneous quaternionic-Kaehler manifolds we find degenerate local minima.

Affiliated with

Also associated with

No associations

Rating

Flows on quaternionic-Kaehler and very special real manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Flows on quaternionic-Kaehler and very special real manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Flows on quaternionic-Kaehler and very special real manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-611278