Black Attractors Research Articles

Intersecting black attractors in 8D [formula omitted] supergravity

We study intersecting extremal black attractors in non-chiral 8D N = 1 supergravity with moduli space SO ( 2 , N ) SO ( 2 ) × SO ( N ) × SO ( 1 , 1 ) and work out explicitly the attractor mechanism for various black p-brane configurations with the typical near horizon geometries AdS p + 2 × S m × T 6 − p − m . We also give the classification of the solutions of the attractor equations in terms of the SO ( N − k ) subgroups of SO ( 2 ) × SO ( N ) symmetry of the moduli space as well as their interpretations in terms of both heterotic string on 2-torus and its type IIA dual. Other features such as non-trivial SO ( 1 , 7 ) central charges Z μ 1 … μ p in 8D N = 1 supergravity and their connections to p-form gauge fields are also given.

On black attractors in 8D and heterotic/type IIA duality

Motivated by the study of black attractors in 8D supergravity with 16 supersymmetries, we use the field theory approach and 8D supersymmetry with non trivial central charges to shed light on the exact duality between heterotic string on T^2 and type IIA on real connected and compact surfaces {\Sigma}2. We investigate the two constraints that should be obeyed by {\Sigma}2 and give their solutions in terms of intersecting 2-cycles as well their classification using Dynkin diagrams of affine Kac-Moody algebras. It is shown as well that the moduli space of these dual theories is given by SO(1,1)x((SO(2,r+2))/(SO(2)xSO(r+2))) where r stands for the rank of the gauge symmetry G_{r} of the 10D heterotic string on T^2. The remarkable cases r=-2,-1,0 as well as other features are also investigated.

On black hole effective potential in 6D/7D [formula omitted] supergravity

Using the harmonic superspace method and the duality between real and complex representations of hypermultiplets, we compute the explicit scalar field expression of the quaternionic metric G m n ( φ ) of the moduli space SO ( 4 , k ) × SO ( 1 , 1 ) SO ( 4 ) × SO ( k ) of 6D N = 2 supergravity with generic k Maxwell supermultiplets. The obtained metric includes the particular case k = 20 associated with 10D type IIA superstring on K3. Uplifting to 7D N = 2 supergravity is described and aspects of 6D/7D black attractor effective potentials are studied.

Formula omitted] supersymmetric black attractors in six and seven dimensions

Using a quaternionic formulation of the moduli space M ( IIA / 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 hyper-Kähler geometry of M ( IIA / K 3 ) and show that the SO ( 4 ) × SO ( 20 ) invariant hyper-Kähler potential is given by H = H 0 + Tr [ ln ( 1 − V 0 −1 S ) ] with Kähler leading term H 0 = Tr [ ln V 0 ] plus an extra term which can be expanded as a power series in V 0 −1 and the traceless and symmetric 3×3 matrix S . We also derive the holomorphic matrix prepotential G and the flux potential G BH of the 6D black objects induced by the topology of the RR field strengths F 2 = d A 1 and F 4 = d A 3 on the K3 surface and show that G BH reads as Q 0 + ∑ m = 1 3 q m Z m . Moreover, we reveal that Z m = ∑ I = 1 20 Q I ( ∫ C 2 I J m ) 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 N = 2 black object attractors in 6D and 7D obtained respectively from type IIA string and M-theory on K3.