Grassmannians, calibrations and five-brane intersections
Nov, 199839 pages
Published in:
- Class.Quant.Grav. 17 (2000) 2641-2662
e-Print:
- hep-th/9811034 [hep-th]
Report number:
- DAMTP-R-98-148
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Abstract:
We present a geometric construction of a new class of hyper-Kahler manifolds with torsion. This involves the superposition of the four-dimensional hyper-Kahler geometry with torsion associated with the NS-5-brane along quaternionic planes in quaternionic k-space, \bH^k. We find the moduli space of these geometries and show that it can be constructed using the bundle space of the canonical quaternionic line bundle over a quaternionic projective space. We also investigate several special cases which are associated with certain classes of quaternionic planes in \bH^k. We then show that the eight-dimensional geometries we have found can be constructed using quaternionic calibrations. We generalize our construction to superpose the same four-dimensional hyper-Kahler geometry with torsion along complex planes in \bC^{2k}. We find that the resulting geometry is Kahler with torsion. The moduli space of these geometries is also investigated. In addition, the applications of these new geometries to M-theory and sigma models are presented. In particular, we find new solutions of IIA supergravity with the interpretation of intersecting NS-5-branes at Sp(2)-angles on a string and show that they preserve 3/32, 1/8, 5/32 and 3/16 of supersymmetry. We also show that two-dimensional sigma models with target spaces the above manifolds have (p,q) extended supersymmetry.- geometry: Kaehler
- torsion
- moduli space
- membrane model
- fibre bundle
- quaternion
- M-theory
- sigma model
- supergravity
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