100,330 research outputs found

    Lodged in the throat: Internal infinities and AdS/CFT

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    In the context of AdS3/CFT2, we address spacetimes with a certain sort of internal infinity as typified by the extreme BTZ black hole. The internal infinity is a null circle lying at the end of the black hole's infinite throat. We argue that such spacetimes may be described by a product CFT of the form CFT-L * CFT-R, where CFT-R is associated with the asymptotically AdS boundary while CFT-L is associated with the null circle. Our particular calculations analyze the CFT dual of the extreme BTZ black hole in a linear toy model of AdS3/CFT2. Since the BTZ black hole is a quotient of AdS3, the dual CFT state is a corresponding quotient of the CFT vacuum state. This state turns out to live in the aforementioned product CFT. We discuss this result in the context of general issues of AdS/CFT duality and entanglement entropy.Comment: 11 pages, 2 figures; v2 - some typos corrected, minor revision

    Thermodynamics of two-dimensional conformal field theory dual to black holes

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    In this note we investigate the first law of thermodynamics of the two-dimensional conformal field theory (CFT) that is dual to black holes. We start from the Cardy formula and get the CFT thermodynamics with minimal reasonable assumptions. We use both the microcanonical ensemble and canonical ensemble versions of the Cardy formula. In the black hole/CFT correspondence the black hole is dual to a CFT with excitations, and the black hole mass MM and charge NN correspond to the energy and charge of the excited CFT. The CFT left- and right-moving central charges cL,Rc_{L,R} should be quantized, and so we assume that they are mass-independent. Also we assume the difference of the left- and right-moving sector levels NLNRN_L-N_R is mass-independent dual to level matching condition. The thermodynamics of two-dimensional CFT we get is universal and supports the thermodynamics method of black hole/CFT correspondence.Comment: 10 page

    Emergence of spacetime from the algebra of total modular Hamiltonians

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    We study the action of the CFT total modular Hamiltonian on the CFT representation of bulk fields with spin. In the vacuum of the CFT the total modular Hamiltonian acts as a bulk Lie derivative, reducing on the RT surface to a boost perpendicular to the RT surface. This enables us to reconstruct bulk fields with spin from the CFT. On fields with gauge redundancies the total modular Hamiltonian acts as a bulk Lie derivative together with a compensating bulk gauge (or diffeomorphism) transformation to restore the original gauge. We consider the Lie algebra generated by the total modular Hamiltonians of all spherical CFT subregions and define weakly-maximal Lie subalgebras as proper subalgebras containing a maximal set of total modular Hamiltonians. In a CFT state with a bulk dual, we show that the bulk spacetime parametrizes the space of these weakly-maximal Lie subalgebras. Each such weakly-maximal Lie subalgebra induces Lorentz transformations at a particular point in the bulk manifold. The bulk metric dual to a pure CFT state is invariant at each point under this transformation. This condition fixes the metric up to a conformal factor that can be computed from knowledge of the equation parametrizing extremal surfaces. This gives a holographic notion of the invariance of a pure CFT state under CFT modular flow.Comment: 27 pages. v2: minor changes. v3: coordinates clarified, version to appear in JHE

    Real-time correlators in warped AdS/CFT correspondence

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    We study real-time correlators in the warped AdS/CFT correspondence. We apply the prescription used in the usual AdS/CFT correspondence and obtain the retarded Green's functions for the scalar and vector fields in the spacelike warped and the null warped black hole backgrounds. We find that the retarded Green's functions and the cross sections are well consistent with the predictions from dual CFT. Our results not only support strongly the conjectured warped AdS/CFT correspondence, but also show that the usual relativistic AdS/CFT prescription of obtaining the real-time correlators remain effective in more general backgrounds with anisotropic conformal infinity.Comment: 27 page

    State/Operator Correspondence in Higher-Spin dS/CFT

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    A recently conjectured microscopic realization of the dS4_4/CFT3_3 correspondence relating Vasiliev's higher-spin gravity on dS4_4 to a Euclidean Sp(N)Sp(N) CFT3_3 is used to illuminate some previously inaccessible aspects of the dS/CFT dictionary. In particular it is argued that states of the boundary CFT3_3 on S2S^2 are holographically dual to bulk states on geodesically complete, spacelike R3R^3 slices which terminate on an S2S^2 at future infinity. The dictionary is described in detail for the case of free scalar excitations. The ground states of the free or critical Sp(N)Sp(N) model are dual to dS-invariant plane-wave type vacua, while the bulk Euclidean vacuum is dual to a certain mixed state in the CFT3_3. CFT3_3 states created by operator insertions are found to be dual to (anti) quasinormal modes in the bulk. A norm is defined on the R3R^3 bulk Hilbert space and shown for the scalar case to be equivalent to both the Zamolodchikov and pseudounitary C-norm of the Sp(N)Sp(N) CFT3_3.Comment: 24 page

    Fantasy proneness and counterfactual thinking

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    Counterfactual thinking (CFT; mentally simulating alternatives to reality) is central to learning and motivation. Two studies explored the relationship between CFT and fantasy proneness, a personality trait typified by excessive fantasies hard to distinguish from reality. In study1, participants completed a fictional diary entry which was used to measure spontaneous CFT and the Creative Experiences Questionnaire measure of fantasy proneness. Fantasy proneness was significantly correlated with the generation of counterfactual thoughts. Both CFT and fantasy proneness have been independently associated with low mood and study2 included a measure of negative emotional state (the Depression, Anxiety and Stress scale) in addition to the CEQ and CFT. Fantasy proneness and negative emotion both predicted CFT, but no interaction between them was observed. The results suggest that individuals high in fantasy proneness have a general tendency to think counterfactually. © 2012 Elsevier Ltd