100,330 research outputs found

### Lodged in the throat: Internal infinities and AdS/CFT

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

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 $M$
and charge $N$ correspond to the energy and charge of the excited CFT. The CFT
left- and right-moving central charges $c_{L,R}$ 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 $N_L-N_R$ 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

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

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

A recently conjectured microscopic realization of the dS$_4$/CFT$_3$
correspondence relating Vasiliev's higher-spin gravity on dS$_4$ to a Euclidean
$Sp(N)$ CFT$_3$ is used to illuminate some previously inaccessible aspects of
the dS/CFT dictionary. In particular it is argued that states of the boundary
CFT$_3$ on $S^2$ are holographically dual to bulk states on geodesically
complete, spacelike $R^3$ slices which terminate on an $S^2$ at future
infinity. The dictionary is described in detail for the case of free scalar
excitations. The ground states of the free or critical $Sp(N)$ model are dual
to dS-invariant plane-wave type vacua, while the bulk Euclidean vacuum is dual
to a certain mixed state in the CFT$_3$. CFT$_3$ states created by operator
insertions are found to be dual to (anti) quasinormal modes in the bulk. A norm
is defined on the $R^3$ bulk Hilbert space and shown for the scalar case to be
equivalent to both the Zamolodchikov and pseudounitary C-norm of the $Sp(N)$
CFT$_3$.Comment: 24 page

### Fantasy proneness and counterfactual thinking

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

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