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Black Hole Entropy Function, Attractors and Precision Counting of Microstates
, 2007
"... In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric strin ..."
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In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric string theories, and compare the statistical entropy of these dyons, expanded in inverse powers of electric and magnetic charges, with a similar expansion of the corresponding black hole entropy. This comparison is extended to include the contribution to the entropy from multicentered black holes as well.
Extremal Black Hole and Flux Vacua Attractors
, 2007
"... These lectures provide a pedagogical, introductory review of the socalled Attractor Mechanism (AM) at work in two different 4dimensional frameworks: extremal black holes in N = 2 supergravity and N = 1 flux compactifications. In the first case, AM determines the stabilization of scalars at the bla ..."
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Cited by 23 (15 self)
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These lectures provide a pedagogical, introductory review of the socalled Attractor Mechanism (AM) at work in two different 4dimensional frameworks: extremal black holes in N = 2 supergravity and N = 1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axiondilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the socalled “criticality conditions ” and “New Attractor ” ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodgedecomposition techniques) is performed, respectively considering 2 CY3×T Type IIB compactified on CY3 and its orientifolded version, associated with. Finally, recent Z2 results on the Uduality orbits and moduli spaces of nonBPS extremal black hole attractors in
WIS/05/08FEBDPP 5D Black Holes and Nonlinear Sigma Models
, 802
"... Abstract: Stationary solutions of 5D supergravity with U(1) isometry can be efficiently studied by dimensional reduction to three dimensions, where they reduce to solutions to a locally supersymmetric nonlinear sigma model. We generalize this procedure to 5D gauged supergravity, and identify the co ..."
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Abstract: Stationary solutions of 5D supergravity with U(1) isometry can be efficiently studied by dimensional reduction to three dimensions, where they reduce to solutions to a locally supersymmetric nonlinear sigma model. We generalize this procedure to 5D gauged supergravity, and identify the corresponding gauging in 3D. We pay particular attention to the case where the Killing spinor is non constant along the fibration, which results, even for ungauged supergravity in 5D, in an additional gauging in 3D, without introducing any extra potential. We further study SU(2) × U(1) symmetric solutions, which correspond to geodesic motion on the sigma model (with potential in the gauged case). We identify and study the algebra of BPS constraints relevant for the BreckenridgeMyersPeetVafa black hole, the GutowskiReall black hole and several other BPS solutions, and obtain the corresponding radial wave functions in the semiclassical approximation. Unité mixte de recherche du CNRS UMR 7589 Unité mixte de recherche du CNRS UMR 8549Contents
GNPHE/0810 On Black Objects in Type IIA Superstring Theory on CalabiYau Manifolds
, 2009
"... The compactification of type IIA superstring on ndimensional CalabiYau manifolds is discussed. In particular, a conjecture is given for type IIA extremal pdimensional black brane attractors corresponding to Adsp+2 × S 8−2n−p horizon geometries. ..."
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The compactification of type IIA superstring on ndimensional CalabiYau manifolds is discussed. In particular, a conjecture is given for type IIA extremal pdimensional black brane attractors corresponding to Adsp+2 × S 8−2n−p horizon geometries.
Almost BPS black holes
, 812
"... k.goldstein [at] uu.nl, s.katmadas [at] uu.nl Abstract: We study nonBPS black hole solutions to ungauged supergravity with 8 supercharges coupled to vector multiplets in four and five dimensions. We identify a large class of five dimensional nonBPS solutions, which we call “almost BPS”, that are s ..."
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k.goldstein [at] uu.nl, s.katmadas [at] uu.nl Abstract: We study nonBPS black hole solutions to ungauged supergravity with 8 supercharges coupled to vector multiplets in four and five dimensions. We identify a large class of five dimensional nonBPS solutions, which we call “almost BPS”, that are supersymmetric on local patches and satisfy a first order flow governed by harmonic functions. By dimensional reduction, they give rise to new nonBPS solutions in four dimensions. These solutions allow for some nontrivial asymptotic moduli and multiple centres, similar to their globally supersymmetric cousins. We explicitly discuss a single centre and a two centre example.
CERNPHTH/2008020 d = 4 Black Hole Attractors in N = 2 Supergravity with FayetIliopoulos Terms
, 802
"... We generalize the description of the d = 4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and th ..."
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We generalize the description of the d = 4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d> 4, as well. Thence, we work out the example of the stu model of N = 2 supergravity in the presence of FayetIliopoulos terms, for the supergravity analogues of the magnetic and D0 − D6 BH charge configurations, and in three different symplectic frames: the (SO (1, 1)) 2, SO (2, 2) covariant and SO (8)truncated ones. The attractive nature of the critical points, related to the semipositive definiteness of the Hessian
Duality symmetry and the Cardy limit
 JHEP 0807, 072 (2008) [arXiv:0711.4671 [hepth
"... Preprint typeset in JHEP style HYPER VERSION ..."
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Observations on Arithmetic Invariants and UDuality Orbits in N = 8 Supergravity
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Lab/UFRHEP0702/GNPHE/0702/VACBT/0702 N = 2 Supersymmetric Black Attractors in Six and Seven Dimensions
, 2008
"... 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 0, 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 ..."
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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 0, 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 m central charges isotriplet of the 6D N = 2 superalgebra. We construct explicitly the special hyperKahler geometry of M (IIA/K3) and show that the SO (4)×SO (20) invariant hyperKahler potential is given by H = H0 + Tr [ ln ( 1 − V −1 0 S)] with Kahler leading term H0 = Tr [ln V 0] plus an extra term which can be expanded as a power series in V −1 0 and the traceless and symmetric 3×3 matrix S. We also derive the holomorphic matrix prepotential G and the flux potential GBH of the 6D black objects induced by the topology of the RR field strengths F2 = dA1 and F4 = dA3 on K3 and show that GBH reads as Q0 + ∑3 m=1 qmZm. Moreover, we reveal that Zm = ∑20