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80
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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Cited by 324 (28 self)
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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.
Split States, Entropy Enigmas, Holes and Halos
, 2007
"... We investigate degeneracies of BPS states of Dbranes on compact CalabiYau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute e ..."
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Cited by 235 (22 self)
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We investigate degeneracies of BPS states of Dbranes on compact CalabiYau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial Dbrane systems, and to clarify the subtle relation of DonaldsonThomas invariants to BPS indices of stable D6D2D0 states, realized in supergravity as “hole halos. ” We introduce a convergent generating function for D4 indices in the large CY volume limit, and prove it can be written as a modular average of its polar part, generalizing the fareytail expansion of the elliptic genus. We show polar states are “split ” D6antiD6 bound states, and that the partition function factorizes accordingly, leading to a refined version of the OSV conjecture. This differs from the original conjecture in several aspects. In particular we obtain a nontrivial measure factor g −2 top e−K and find factorization requires a cutoff. We show that the main factor determining the cutoff and therefore the error is the existence of “swing states ” — D6 states which exist at large radius but do not form stable D6antiD6 bound states. We point out a likely breakdown of the OSV conjecture at small gtop (in the large background CY volume limit), due to the surprising phenomenon that for sufficiently large background Kähler moduli, a charge ΛΓ supporting single centered black holes of entropy ∼ Λ2S(Γ) also admits twocentered BPS black hole realizations whose entropy grows like Λ3 when Λ → ∞.
Microscopic black hole entropy in theories with higher derivatives
"... We discuss higher derivative corrections to black hole entropy in theories that allow a near horizon AdS3 × X geometry. In arbitrary theories with diffeomorphism invariance we show how to obtain the spacetime central charge in a simple way. Black hole entropy then follows from the Euclidean partitio ..."
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Cited by 116 (15 self)
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We discuss higher derivative corrections to black hole entropy in theories that allow a near horizon AdS3 × X geometry. In arbitrary theories with diffeomorphism invariance we show how to obtain the spacetime central charge in a simple way. Black hole entropy then follows from the Euclidean partition function, and we show that this gives agreement with Wald’s formula. In string theory there are certain diffeomorphism anomalies that we exploit. We thereby reproduce some recent computations of corrected entropy formulas, and extend them to the nonextremal, nonsupersymetric context. Examples include black holes in Mtheory on K3×T 2, whose entropy reproduces that of the perturbative heterotic string with both right and left movers excited and angular momentum included. Our anomaly based approach also sheds light on why exact results have been obtained in four dimensions while ignoring R 4 type corrections.
Holographic gravitational anomalies
 JHEP
, 2006
"... In the AdS/CFT correspondence one encounters theories that are not invariant under diffeomorphisms. In the boundary theory this is a gravitational anomaly, and can arise in 4k + 2 dimensions. In the bulk, there can be gravitational ChernSimons terms which vary by a total derivative. We work out the ..."
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Cited by 102 (7 self)
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In the AdS/CFT correspondence one encounters theories that are not invariant under diffeomorphisms. In the boundary theory this is a gravitational anomaly, and can arise in 4k + 2 dimensions. In the bulk, there can be gravitational ChernSimons terms which vary by a total derivative. We work out the holographic stress tensor for such theories, and demonstrate agreement between the bulk and boundary. Anomalies lead to novel effects, such as a nonzero angular momentum for global AdS3. In string theory such ChernSimons terms are known with exact coefficients. The resulting anomalies, combined with symmetries, imply corrections to the BekensteinHawking entropy of black holes that agree exactly with the microscopic counting.
Lectures on on black holes, topological strings and quantum attractors
, 2006
"... Preprint typeset in JHEP style PAPER VERSION hepth/0607227 ..."
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Cited by 62 (10 self)
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Preprint typeset in JHEP style PAPER VERSION hepth/0607227
New attractor, entropy function and black hole partition function
 JHEP
"... By making use of the entropy function formalism we study the generalized attractor equations in the four dimensional N = 2 supergravity in the presence of higher order corrections. This result might be used to understand a possible ensemble one could associate to an extremal black hole. Using the ge ..."
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Cited by 43 (2 self)
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By making use of the entropy function formalism we study the generalized attractor equations in the four dimensional N = 2 supergravity in the presence of higher order corrections. This result might be used to understand a possible ensemble one could associate to an extremal black hole. Using the generality and simplicity of this formalism we establish a duality between a four gravitational theory on AdS2 × S 2 background and the extremal black hole of the theory whose near horizon geometry is fixed by the AdS2 background. In this sense the attractor mechanism plays the role of decoupling limit in the context of AdS/CFT correspondence.
BPS black hole degeneracies and minimal automorphic representations
 JHEP
"... Preprint typeset in JHEP style PAPER VERSION hepth/0506228 ..."
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Cited by 42 (11 self)
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Preprint typeset in JHEP style PAPER VERSION hepth/0506228