N=2 Supersymmetric Black Attractors in Six and Seven Dimensions

A. Belhaj; L. B. Drissi; E. H. Saidi; A. Segui

doi:10.1016/j.nuclphysb.2007.12.007

paper

N=2 Supersymmetric Black Attractors in Six and Seven Dimensions

arXiv:0709.0398 · doi:10.1016/j.nuclphysb.2007.12.007

Abstract

Using a quaternionic formulation of the moduli space $M (I I A / K 3)$ of 10D type IIA superstring on a generic K3 complex surface with volume $V_{0}$ , we study extremal $N = 2$ black attractors in 6D space-time and their uplifting to 7D. For the 6D theory, we exhibit the role played by 6D $N = 1$ hypermultiplets and the $Z^{m}$ central charges isotriplet of the 6D $N = 2$ superalgebra. We construct explicitly the special hyperKahler geometry of and show that the $S O (4) \times S O (20)$ invariant hyperKahler potential is given by $H = H_{0} + Tr [ln (1 -$ with Kahler leading term $H_{0} = Tr [ln V_{0}]$ plus an extra term which can be expanded as a power series in $V$ and the traceless and symmetric 3 $\times$ 3 matrix $S$ . We also derive the holomorphic matrix prepotential $G$ and the flux potential $G_{B H}$ of the 6D black objects induced by the topology of the RR field strengths $F_{2} = d A_{1}$ and on the K3 surface and show that $\mathcal{G% }_{BH}$ reads as $Q_{0} + \sum_{m = 1}^{3} q^{m} Z^{m}$ . Moreover, we reveal that where the isotriplet $J^{m}$ is the hyperKahler 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-th].

71 pages, Sections 6 and 7 added, References added

N=2 Supersymmetric Black Attractors in Six and Seven Dimensions

Abstract

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