Operator content of two-dimensional conformally invariant theories

Black holes whose near-horizon geometries are locally, but not necessarily globally, AdS 3 (three-dimensional anti-de Sitter space) are considered. Using the fact that quantum gravity on AdS 3 is a conformal field theory, we microscopically compute the black hole entropy from the asymptotic growth of states. Precise numerical agreement with the Bekenstein-Hawking area formula for the entropy is found. The result pertains to any consistent quantum theory of gravity, and does not use string theory or supersymmetry.

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“…The asymptotic growth of the number states of a conformal field theory with central charge c is then given by [14] …”

Section: Microscopic Derivation Of the Black Hole Entropymentioning

confidence: 99%

Black hole entropy from near-horizon microstates

Strominger¹

1998

J. High Energy Phys.

1,041

1,571

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“…A more satisfactory explanation is that in general the central charge is not a good measure of the number of degrees of freedom. For example, if one does not assume normalizability of vacuum, Cardy's formula [20] says that the growth of the density of states is determined not by c, but by c ef f = c − 24h min , where h min is the lower boundary of the spectrum of L 0 . 1 If a unitary CFT has a normalizable vacuum, then h min = 0, but in general the effective number of degrees of freedom is different from c. For the supercoset model h min = 1 4k (this can be derived either by using the fact that the supercoset is asymptotic to a linear dilaton theory with background charge Q = 1/ √ k and applying the Seiberg bound [18], or by the direct analysis of the operator spectrum), and therefore c ef f = 3.…”

Section: Jhep08(2001)045mentioning

confidence: 99%

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry

Hori

Kapustin

2001

J. High Energy Phys.

218

427

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Abstract:We prove the equivalence of the SL(2, R)/ U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N = 2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the charged scalar fields and taking into account the vortex-instanton effects, as proposed recently in non-dilatonic models. The gauged linear sigma-model we study has many useful generalizations which we briefly discuss. In particular, we show how to construct a variety of dilatonic superstring backgrounds which generalize the fermionic 2d Black Hole and admit a mirror description in terms of Toda-like theories.

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“…Recently, Verlinde [24] drew an interesting analogy between the FRW equations of a standard, closed, radiationdominated universe and the two-dimensional entropy formula due to Cardy [25]. In this Section, we will extend this analogy to the FRW equations under consideration.…”

Section: Cosmological Entropy and Generalized Cardy-verlinde Formulamentioning

confidence: 97%

“…In the next Section, we consider the physical interpretation of the Friedmann equation (3.9) in more detail and investigate whether an analogy can be made between this equation and a generalized Cardy-Verlinde formula [24,25].…”

Section: Brane Dynamics In Asymptotically Ds Spacementioning

confidence: 99%

Braneworld cosmology in (anti)-de Sitter Einstein-Gauss-Bonnet-Maxwell gravity

Lidsey¹,

Nojiri²,

Odintsov³

2002

J. High Energy Phys.

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Braneworld cosmology for a domain wall embedded in the charged (Anti)-de Sitter-Schwarzschild black hole of the five-dimensional Einstein-GaussBonnet-Maxwell theory is considered. The effective Friedmann equation for the brane is derived by introducing the necessary surface counterterms required for a well-defined variational principle in the Gauss-Bonnet theory and for the finiteness of the bulk space. The asymptotic dynamics of the brane cosmology is determined and it is found that solutions with vanishingly small spatial volume are unphysical. The finiteness of the bulk action is related to the vanishing of the effective cosmological constant on the brane. An analogy between the Friedmann equation and a generalized Cardy-Verlinde formula is drawn.

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Operator content of two-dimensional conformally invariant theories

Cited by 1,806 publications

References 15 publications

Black hole entropy from near-horizon microstates

Black hole entropy from near-horizon microstates

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry

Braneworld cosmology in (anti)-de Sitter Einstein-Gauss-Bonnet-Maxwell gravity

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