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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 326 (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 241 (21 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 → ∞.
4d/5d Correspondence for the Black Hole Potential and its Critical
"... We express the d = 4, N = 2 black hole effective potential for cubic holomorphic F functions and generic dyonic charges in terms of d = 5 real special geometry data. The 4d critical points are computed from the 5d ones, and their relation is elucidated. For symmetric spaces, we identify the BPS and ..."
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Cited by 42 (23 self)
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We express the d = 4, N = 2 black hole effective potential for cubic holomorphic F functions and generic dyonic charges in terms of d = 5 real special geometry data. The 4d critical points are computed from the 5d ones, and their relation is elucidated. For symmetric spaces, we identify the BPS and nonBPS classes of attractors and the respective entropies. These always derive from simple interpolating formulæ between four and five dimensions, depending on the volume Recently there has been an increasing amount of work on extremal charged black holes in an environment of scalar background fields, as they naturally arise in modern theories of gravity: superstrings, Mtheory, and their lowenergy description through supergravity. In particular, the Attractor
5D attractors with higher derivatives
 JHEP
, 2007
"... We analyze higher derivative corrections to attractor geometries in five dimensions. We find corrected AdS3 × S2 geometries by solving the equations of motion coming from a recently constructed fourderivative supergravity action in five dimensions. The result allows us to explicitly verify a previo ..."
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Cited by 28 (6 self)
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We analyze higher derivative corrections to attractor geometries in five dimensions. We find corrected AdS3 × S2 geometries by solving the equations of motion coming from a recently constructed fourderivative supergravity action in five dimensions. The result allows us to explicitly verify a previous anomaly based derivation of the AdS3 central charges of this theory. Also, by dimensional reduction we compare our results with those of the 4D higher derivative attractor, and find complete agreement.
Riet, The full integration of black hole solutions to symmetric supergravity theories
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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 23 (8 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
Precision entropy of spinning black holes
 JHEP 0709, 003 (2007) [arXiv:0705.1847 [hepth
"... We construct spinning black hole solutions in five dimensions that take into account the mixed gaugegravitational ChernSimons term and its supersymmetric completion. The resulting entropy formula is discussed from several points of view. We include a TaubNUT base space in order to test recent con ..."
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Cited by 22 (3 self)
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We construct spinning black hole solutions in five dimensions that take into account the mixed gaugegravitational ChernSimons term and its supersymmetric completion. The resulting entropy formula is discussed from several points of view. We include a TaubNUT base space in order to test recent conjectures relating 5D black holes to 4D black holes and the topological string. Our explicit results show that certain charge shifts have to be taken into account for these relations to hold. We also compute corrections to the entropy of black rings in terms of near horizon data.
Instabilities of Black Strings and Branes
 INVITED REVIEW FOR CLASSICAL AND QUANTUM GRAVITY
, 2007
"... We review recent progress on the instabilities of black strings and branes both for pure Einstein gravity as well as supergravity theories which are relevant for string theory. We focus mainly on GregoryLaflamme instabilities. In the first part of the review we provide a detailed discussion of the ..."
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Cited by 21 (1 self)
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We review recent progress on the instabilities of black strings and branes both for pure Einstein gravity as well as supergravity theories which are relevant for string theory. We focus mainly on GregoryLaflamme instabilities. In the first part of the review we provide a detailed discussion of the classical gravitational instability of the neutral uniform black string in higher dimensional gravity. The uniform black string is part of a larger phase diagram of KaluzaKlein black holes which will be discussed thoroughly. This phase diagram exhibits many interesting features including new phases, nonuniqueness and horizontopology changing transitions. In the second part, we turn to charged black branes in supergravity and show how the GregoryLaflamme instability of the neutral black string implies via a boost/Uduality map similar instabilities for non and nearextremal smeared branes in string theory. We also comment on instabilities of Dbrane bound states. The connection between classical and thermodynamic stability, known as the correlated stability conjecture, is also reviewed and illustrated with examples. Finally, we examine the holographic implications of the GregoryLaflamme instability for a number of nongravitational theories including YangMills theories and Little String Theory.
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 21 (10 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
The automorphic NS5brane
, 2009
"... Understanding the implications of SL(2, Z) Sduality on the hypermultiplet moduli space of type II string theories has led to much progress recently in uncovering Dinstanton contributions. In this note, we suggest that the extended duality group SL(3, Z), which includes both Sduality and Ehlers s ..."
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Cited by 20 (10 self)
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Understanding the implications of SL(2, Z) Sduality on the hypermultiplet moduli space of type II string theories has led to much progress recently in uncovering Dinstanton contributions. In this note, we suggest that the extended duality group SL(3, Z), which includes both Sduality and Ehlers symmetry, potentially determines the contributions of NS5branes. We support this claim by automorphizing the perturbative corrections to the “extended universal hypermultiplet”, a fivedimensional universal SO(3)\SL(3) subspace which includes the string coupling, overall volume, Ramond zeroform and sixform and NS axion. In particular, we show that NS5brane contributions are encoded by nonAbelian Fourier coefficients and satisfy a wave function property. We also conjecture that for models with a symmetric moduli space, the partition function of any number of NS5branes is given by the minimal theta series of the corresponding duality group.