supersymmetric black attractors in six and seven dimensions

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• 作者：A. Belhaj ; L.B. Drissi ; E.H. Saidi ; A. Segui
• 关键词：Type IIA superstring on the K3 surface ; Special hyper-Kä ; hler geometry ; 6D/7D Nuclear Physics B
• 出版年：2008
• 期刊代码：45_05503213
• 类别：ph
• 出版时间：21 June 2008
• 卷：796
• 期：3
• 页码：521-580
• 文件大小：483 K

摘要

Using a quaternionic formulation of the moduli space M (IIA/K3) of 10D type IIA superstring on a generic K3 complex surface with volume V₀, we study extremal black attractors in 6D space–time and their uplifting to 7D. For the 6D theory, we exhibit the role played by 6D a20baab563e"> hypermultiplets and the Z^m central charges isotriplet of the 6D superalgebra. We construct explicitly the special hyper-Kähler geometry of M (IIA/K3) and show that the SO(4)×SO(20) invariant hyper-Kähler potential is given by with Kähler leading term plus an extra term which can be expanded as a power series in and the traceless and symmetric 3×3 matrix S. We also derive the holomorphic matrix prepotential and the flux potential of the 6D black objects induced by the topology of the RR field strengths and on the K3 surface and show that reads as . Moreover, we reveal that where the isotriplet J^m is the hyper-Kähler 2-form on the K3 surface. It is found as well that the uplifting to seven dimensions is quite similar to 4D/5D correspondence for back hole potential considered in arXiv: 0707.0964 [hep-ph]. Then we study the black object attractors in 6D and 7D obtained respectively from type IIA string and M-theory on K3.