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318
Axiomatic quantum field theory in curved spacetime
, 2008
"... The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globa ..."
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Cited by 687 (18 self)
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The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spinstatistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.
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.
Covariant Theory of Asymptotic Symmetries, Conservation Laws and Central Charges
, 2001
"... Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between non trivial asymptotic reducibility parameters and non trivial asymptotically conserved n 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters ar ..."
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Cited by 132 (17 self)
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Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between non trivial asymptotic reducibility parameters and non trivial asymptotically conserved n 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters are the parameters of gauge transformations that vanish suciently fast when evaluated at the background. A universal formula for asymptotically conserved n 2 forms in terms of the reducibility parameters is derived. Sucient conditions for niteness of the charges built out of the asymptotically conserved n 2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, YangMills theory and Einstein gravity where they reproduce familiar results.
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 132 (9 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
Holographic Entanglement Entropy: An Overview
, 2009
"... In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole ..."
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Cited by 120 (12 self)
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In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.
Increase of Black Hole Entropy in Higher Curvature Gravity
"... We discuss some recent results on black hole thermodynamics within the context of effective gravitational actions including highercurvature interactions. Wald’s derivation of the First Law demonstrates that black hole entropy can always be expressed as a local geometric density integrated over a sp ..."
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Cited by 118 (11 self)
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We discuss some recent results on black hole thermodynamics within the context of effective gravitational actions including highercurvature interactions. Wald’s derivation of the First Law demonstrates that black hole entropy can always be expressed as a local geometric density integrated over a spacelike crosssection of the horizon. In certain cases, it can also be shown that these entropy expressions satisfy a Second Law. One such simple example is considered from the class of higher curvature theories where the Lagrangian consists of a polynomial in the Ricci scalar. 1.
The Thermodynamics of Black Holes
, 2000
"... We review the present status of black hole thermodynamics. Our review includes discussion of classical black hole thermodynamics, Hawking radiation from black holes, the generalized second law, and the issue of entropy bounds. A brief survey also is given of approaches to the calculation of black ho ..."
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Cited by 106 (1 self)
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We review the present status of black hole thermodynamics. Our review includes discussion of classical black hole thermodynamics, Hawking radiation from black holes, the generalized second law, and the issue of entropy bounds. A brief survey also is given of approaches to the calculation of black hole entropy. We conclude with a discussion of some unresolved open issues.
Curvature singularities: The good, the bad, and the naked
 Adv. Theor. Math. Phys
, 2002
"... Necessary conditions are proposed for the admissibility of singular classical solutions with 3 + 1dimensional Poincaré invariance to fivedimensional gravity coupled to scalars. Finite temperature considerations and examples from AdS/CFT support the conjecture that the scalar potential must remain ..."
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Cited by 99 (7 self)
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Necessary conditions are proposed for the admissibility of singular classical solutions with 3 + 1dimensional Poincaré invariance to fivedimensional gravity coupled to scalars. Finite temperature considerations and examples from AdS/CFT support the conjecture that the scalar potential must remain bounded above for a solution to be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem. In AdS/CFT [1, 2, 3] (see [4] for a review), bulk geometries which are only asymptotically AdS5 near the timelike boundary are dual to relevant deformations of the CFT or to nonconformal vacua. Far from the timelike boundary, various singularities might arise. There must be some restrictions on the type of singularity which is allowed: for
Exact and Asymptotic Degeneracies of Small Black Holes
, 2005
"... We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative heterotic BPS states. In several examples with N = 4 and N = 2 supersymmetry, we show that the macrosc ..."
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Cited by 80 (12 self)
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We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative heterotic BPS states. In several examples with N = 4 and N = 2 supersymmetry, we show that the macroscopic degeneracy of small black holes agrees to all orders with the microscopic degeneracy, but misses nonperturbative corrections which are computable in the heterotic dual. Using these examples we refine the previous proposals and comment on their domain of validity as well as on the relevance of helicity supertraces.