N=2 supersymmetric black attractors in six and seven dimensions
Abstract
Using a quaternionic formulation of the moduli space M(IIA/K3) of 10D type IIA superstring on a generic K3 complex surface with volume V, we study extremal N=2 black attractors in 6D spacetime and their uplifting to 7D. For the 6D theory, we exhibit the role played by 6D N=1 hypermultiplets and the Z central charges isotriplet of the 6D N=2 superalgebra. We construct explicitly the special hyperKähler geometry of M(IIA/K3) and show that the SO(4)×SO(20) invariant hyperKähler potential is given by H=H+Tr[ln(1V01S)] with Kähler leading term H=Tr[lnV] plus an extra term which can be expanded as a power series in V01 and the traceless and symmetric 3×3 matrix S. We also derive the holomorphic matrix prepotential G and the flux potential G of the 6D black objects induced by the topology of the RR field strengths F=dA and F=dA on the K3 surface and show that G reads as Q+∑m=13qZ. Moreover, we reveal that Z=∑I=120Q(∫J) where the isotriplet J is the hyperKähler 2form 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 [hepph]. Then we study the N=2 black object attractors in 6D and 7D obtained respectively from type IIA string and Mtheory on K3.
 Publication:

Nuclear Physics B
 Pub Date:
 June 2008
 DOI:
 10.1016/j.nuclphysb.2007.12.007
 arXiv:
 arXiv:0709.0398
 Bibcode:
 2008NuPhB.796..521B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 71 pages, Sections 6 and 7 added, References added