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72
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
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
Two centered black holes and N=4 dyon spectrum
"... The exact spectrum of dyons in a class of N=4 supersymmetric string theories is known to change discontinuously across walls of marginal stability. We show that the change in the degeneracy across the walls of marginal stability can be accounted for precisely by the entropy ..."
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Cited by 30 (16 self)
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The exact spectrum of dyons in a class of N=4 supersymmetric string theories is known to change discontinuously across walls of marginal stability. We show that the change in the degeneracy across the walls of marginal stability can be accounted for precisely by the entropy
R 4 corrections to D1D5p black hole entropy from entropy function formalism
"... We show that in IIB string theory and for D1D5p black holes in ten dimensions the method of entropy function works. Despite the more complicated Wald formula for the entropy of D1D5p black holes in ten dimensions, their entropy is given by entropy function at its extremum point. We use this method f ..."
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Cited by 24 (1 self)
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We show that in IIB string theory and for D1D5p black holes in ten dimensions the method of entropy function works. Despite the more complicated Wald formula for the entropy of D1D5p black holes in ten dimensions, their entropy is given by entropy function at its extremum point. We use this method for computing the entropy of the system both at the level of Black holes in string theory can be constructed out of various Dbrane configurations. This is a well known result that the entropy of these black holes can be computed from the Wald formula [1], [2]. Further more it has been shown that this entropy is in exact agreement with counting the degeneracy of the microstates of