3,464 research outputs found
Entropy in Spin Foam Models: The Statistical Calculation
Recently an idea for computing the entropy of black holes in the spin foam
formalism has been introduced. Particularly complete calculations for the three
dimensional euclidean BTZ black hole were done. The whole calculation is based
on observables living at the horizon of the black hole universe. Departing from
this idea of observables living at the horizon, we now go further and compute
the entropy of BTZ black hole in the spirit of statistical mechanics. We
compare both calculations and show that they are very interrelated and equally
valid. This latter behaviour is certainly due to the importance of the
observables.Comment: 11 pages, 1 figur
One point functions for black hole microstates
We compute one point functions of chiral primary operators in the D1-D5
orbifold CFT, in classes of states corresponding to microstates of two and
three charge black holes. Black hole microstates describable by supergravity
solutions correspond to coherent superpositions of states in the orbifold
theory and we develop methods for approximating one point functions in such
superpositions in the large N limit. We show that microstates built from long
strings (large twist operators) have one point functions that are suppressed by
powers of N. Accordingly, even when these microstates admit supergravity
descriptions, the characteristic scales in these solutions are comparable to
higher derivative corrections to supergravity.Comment: 74 page
Flux-area operator and black hole entropy
We show that, for space-times with inner boundaries, there exists a natural
area operator different from the standard one used in loop quantum gravity.
This new flux-area operator has equidistant eigenvalues. We discuss the
consequences of substituting the standard area operator in the
Ashtekar-Baez-Corichi-Krasnov definition of black hole entropy by the new one.
Our choice simplifies the definition of the entropy and allows us to consider
only those areas that coincide with the one defined by the value of the level
of the Chern-Simons theory describing the horizon degrees of freedom. We give a
prescription to count the number of relevant horizon states by using spin
components and obtain exact expressions for the black hole entropy. Finally we
derive its asymptotic behavior, discuss several issues related to the
compatibility of our results with the Bekenstein-Hawking area law and the
relation with Schwarzschild quasi-normal modes.Comment: 25 page
The Library of Babel: On the origin of gravitational thermodynamics
We show that heavy pure states of gravity can appear to be mixed states to
almost all probes. For AdS_5 Schwarzschild black holes, our arguments are made
using the field theory dual to string theory in such spacetimes. Our results
follow from applying information theoretic notions to field theory operators
capable of describing very heavy states in gravity. For half-BPS states of the
theory which are incipient black holes, our account is exact: typical
microstates are described in gravity by a spacetime ``foam'', the precise
details of which are almost invisible to almost all probes. We show that
universal low-energy effective description of a foam of given global charges is
via certain singular spacetime geometries. When one of the specified charges is
the number of D-branes, the effective singular geometry is the half-BPS
``superstar''. We propose this as the general mechanism by which the effective
thermodynamic character of gravity emerges.Comment: LaTeX, 6 eps figures, uses young.sty and wick.sty; Version 2: typos
corrected, minor rewordings and clarifications, references adde
Area law for random graph states
Random pure states of multi-partite quantum systems, associated with
arbitrary graphs, are investigated. Each vertex of the graph represents a
generic interaction between subsystems, described by a random unitary matrix
distributed according to the Haar measure, while each edge of the graph
represents a bi-partite, maximally entangled state. For any splitting of the
graph into two parts we consider the corresponding partition of the quantum
system and compute the average entropy of entanglement. First, in the special
case where the partition does not "cross" any vertex of the graph, we show that
the area law is satisfied exactly. In the general case, we show that the
entropy of entanglement obeys an area law on average, this time with a
correction term that depends on the topologies of the graph and of the
partition. The results obtained are applied to the problem of distribution of
quantum entanglement in a quantum network with prescribed topology.Comment: v2: minor typos correcte
Entanglement, quantum randomness, and complexity beyond scrambling
Scrambling is a process by which the state of a quantum system is effectively
randomized due to the global entanglement that "hides" initially localized
quantum information. In this work, we lay the mathematical foundations of
studying randomness complexities beyond scrambling by entanglement properties.
We do so by analyzing the generalized (in particular R\'enyi) entanglement
entropies of designs, i.e. ensembles of unitary channels or pure states that
mimic the uniformly random distribution (given by the Haar measure) up to
certain moments. A main collective conclusion is that the R\'enyi entanglement
entropies averaged over designs of the same order are almost maximal. This
links the orders of entropy and design, and therefore suggests R\'enyi
entanglement entropies as diagnostics of the randomness complexity of
corresponding designs. Such complexities form a hierarchy between information
scrambling and Haar randomness. As a strong separation result, we prove the
existence of (state) 2-designs such that the R\'enyi entanglement entropies of
higher orders can be bounded away from the maximum. However, we also show that
the min entanglement entropy is maximized by designs of order only logarithmic
in the dimension of the system. In other words, logarithmic-designs already
achieve the complexity of Haar in terms of entanglement, which we also call
max-scrambling. This result leads to a generalization of the fast scrambling
conjecture, that max-scrambling can be achieved by physical dynamics in time
roughly linear in the number of degrees of freedom.Comment: 72 pages, 4 figures. Rewritten version with new title. v3: published
versio
Entropy of near-extremal black holes in AdS_5
We construct the microstates of near-extremal black holes in AdS_5 x S^5 as
gases of defects distributed in heavy BPS operators in the dual SU(N)
Yang-Mills theory. These defects describe open strings on spherical D3-branes
in the S^5, and we show that they dominate the entropy by directly enumerating
them and comparing the results with a partition sum calculation. We display new
decoupling limits in which the field theory of the lightest open strings on the
D-branes becomes dual to a near-horizon region of the black hole geometry. In
the single-charge black hole we find evidence for an infrared duality between
SU(N) Yang-Mills theories that exchanges the rank of the gauge group with an
R-charge. In the two-charge case (where pairs of branes intersect on a line),
the decoupled geometry includes an AdS_3 factor with a two-dimensional CFT
dual. The degeneracy in this CFT accounts for the black hole entropy. In the
three-charge case (where triples of branes intersect at a point), the decoupled
geometry contains an AdS_2 factor. Below a certain critical mass, the
two-charge system displays solutions with naked timelike singularities even
though they do not violate a BPS bound. We suggest a string theoretic
resolution of these singularities.Comment: LaTeX; v2: references and a few additional comments adde
The fuzzball proposal for black holes: an elementary review
We give an elementary review of black holes in string theory. We discuss BPS
holes, the microscopic computation of entropy and the `fuzzball' picture of the
black hole interior suggested by microstates of the 2-charge system.Comment: 45 pages, 2 figures; Lecture given at the RTN workshop `The quantum
structure of space-time and the geometric nature of fundamental
interactions', in Crete, Greece (September 2004
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