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833
Large N field theories, string theory and gravity
, 2001
"... We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evide ..."
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Cited by 1474 (45 self)
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We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and nonconformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.
Antide Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories
 Adv. Theor. Math. Phys
, 1998
"... The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum phenome ..."
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Cited by 1087 (4 self)
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The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale “holographically ” with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry. March
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 → ∞.
The dS/CFT correspondence
 JHEP
, 2001
"... A holographic duality is proposed relating quantum gravity on dSD (Ddimensional de Sitter space) to conformal field theory on a single SD−1 ((D1)sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I + (the future bou ..."
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Cited by 201 (7 self)
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A holographic duality is proposed relating quantum gravity on dSD (Ddimensional de Sitter space) to conformal field theory on a single SD−1 ((D1)sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I + (the future boundary of dSD) are mapped to the antipodal points on SD−1 relative to those on I −. For the case of dS3, which is analyzed in some detail, the central charge of the CFT2 is computed in an analysis of the asymptotic symmetry group at I ±. This dS/CFT proposal is supported by the computation of correlation functions of a massive scalar field. In general the dual CFT may be nonunitary and (if for example there are sufficently massive stable scalars) contain complex conformal weights. We also consider the physical region O − of dS3 corresponding to the causal past of a timelike observer, whose holographic dual lives on a plane rather than a sphere. O − can be foliated by asymptotically flat spacelike slices. Time evolution along these slices is generated by
Supersymmetry and Attractors
 Phys. Rev. D
, 1996
"... We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the modul ..."
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Cited by 161 (14 self)
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We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the moduli space (a minimum corresponds to a fixed point of attraction). The extremal value of the square of the central charge provides the area of the horizon, which depends only on electric and magnetic charges. The doubling of unbroken supersymmetry at the fixed point of attraction for N=2 black holes near the horizon is derived via conformal flatness of the BertottiRobinsontype geometry. These results provide an explicit model independent expression for the macroscopic BekensteinHawking entropy of N=2 black holes which is manifestly duality invariant. The presence of hypermultiplets in the solution does not affect the area formula. Various examples of the general formula are displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the relation to the N=2 case. The entropyarea formula in five dimensions, recently discussed in the literature, is also seen to be obtained by extremizing the 5d central charge.
Dbranes and short distances in string theory
"... We study the behavior of Dbranes at distances far shorter than the string length scale ls. We argue that shortdistance phenomena are described by the IR behavior of the Dbrane worldvolume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupli ..."
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Cited by 147 (8 self)
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We study the behavior of Dbranes at distances far shorter than the string length scale ls. We argue that shortdistance phenomena are described by the IR behavior of the Dbrane worldvolume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling gs this corresponds to momenta and energies far above string scale. We use 0brane quantum mechanics to study 0brane collisions and find structure at length scales corresponding to the elevendimensional Planck length (l 11 P ∼ g1/3 s ls) and to the radius of the eleventh dimension in Mtheory (R11 ∼ gsls). We use 0branes to probe nontrivial geometries and topologies at substringy scales. We study the 0brane 4brane system, calculating the 0brane moduli space metric, and find the bound state at threshold, which has characteristic size l11 P. We examine the blowup of an orbifold and are able to resolve the resulting S2 down to size l11 P. A 0brane with momentum approaching 1/R11 is able to explore a larger configuration space in which the blowup is embedded. Analogous phenomena occur for small instantons. We finally turn to 1branes and calculate the size of a bound state to be ∼ g 1/2 s ls, the 1brane tension scale. August
Boundary deformation theory and moduli spaces of Dbranes
, 1999
"... Boundary conformal field theory is the suitable framework for a microscopic treatment of Dbranes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions generated by marginal boundary fields. The deformation parameters ..."
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Cited by 142 (27 self)
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Boundary conformal field theory is the suitable framework for a microscopic treatment of Dbranes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions generated by marginal boundary fields. The deformation parameters may be regarded as continuous moduli of Dbranes. We identify a large class of boundary fields which are shown to be truly marginal, and we derive closed formulas describing the associated deformations to all orders in perturbation theory. This allows us to study the global topology properties of the moduli space rather than local aspects only. As an example, we analyse in detail the moduli space of c = 1 theories, which displays various stringy phenomena.
The holographic principle
 Rev. Mod. Phys
, 2002
"... There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 1.4 ×10 69 bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black hole ..."
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Cited by 125 (7 self)
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There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 1.4 ×10 69 bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of lightsheets, which associate relevant spacetime regions to any