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64
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 → ∞.
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
Product representation of dyon partition function in chl models
"... Preprint typeset in JHEP style HYPER VERSION hepth/0602254 ..."
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Cited by 61 (23 self)
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Preprint typeset in JHEP style HYPER VERSION hepth/0602254
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.
Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
, 2008
"... We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of ..."
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Cited by 34 (9 self)
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We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry, – named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical
Spectrum of dyons and black holes in CHL orbifolds using borcherds lift
, 2007
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Quantum covariant cmap
 JHEP
"... We generalize the results of hepth/0701214 about the covariant cmap to include the perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkähler cone obtained by the quantum cmap to the quaternionKähler space, which is the moduli space of hypermult ..."
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Cited by 21 (10 self)
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We generalize the results of hepth/0701214 about the covariant cmap to include the perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkähler cone obtained by the quantum cmap to the quaternionKähler space, which is the moduli space of hypermultiplets. As a result, the perturbatively corrected metric on the moduli space is found in a simplified form comparing to the expression known in the literature. 1
Large Dinstanton effects in string theory,” arXiv:0904.2303 [hepth
"... Abstract: By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order exp(−Q/gs) to certain protected couplings in the threedimensional effective action, but the number of distinct instantons is ex ..."
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Cited by 19 (8 self)
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Abstract: By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order exp(−Q/gs) to certain protected couplings in the threedimensional effective action, but the number of distinct instantons is expected to be equal (or comparable) to the number of black hole microstates, i.e. of order exp(Q2). The same phenomenon also occurs for certain protected couplings in four dimensions, such as the hypermultiplet metric in type II string theories compactified on a CalabiYau threefold. In either case, the Dinstanton series is therefore asymptotic, much like the perturbative expansion in any quantum field theory. By using a Boreltype resummation method, adapted to the Gaussian growth of the Dinstanton series, we find that the total Dinstanton sum has an inherent ambiguity of order exp(−1/g2 s). We further suggest that this ambiguity can be lifted by including KaluzaKlein monopole or NS5brane instantons. The large order behavior of perturbation theory is a telltale hint on the nature of nonperturbative effects in quantum mechanics and quantum field theory [1, 2, 3]. This also holds for string theory, and indeed, an estimate of the growth of string perturbation theory [4] led to the prediction of the existence of Dbrane instantons [5] long before their actual construction [6, 7, 8]. Dinstantons contribute to scattering amplitudes A in string theory on R1,d−1 × Y schematically as Ainst(gs, t a, θI) = ∑ Q I ∈L µ(Q I, gs, t a) exp − 1
Nonsupersymmetric Black Holes and Topological Strings
, 2007
"... We study nonsupersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on CalabiYau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the nonsupersymmetric black hole entropy, in terms of the one pa ..."
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Cited by 18 (1 self)
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We study nonsupersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on CalabiYau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the nonsupersymmetric black hole entropy, in terms of the one parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for nonsupersymmetric black holes and show how the inverse problem of fixing charges in terms of the attractor value of CY moduli can be explicitly solved.