Fortschritte der Physik

Cover image for Vol. 64 Issue 2-3

Editor: Dieter Lüst, Wolfgang Schleich (Co-Editor)

Impact Factor: 2.442

ISI Journal Citation Reports © Ranking: 2014: 17/78 (Physics Multidisciplinary)

Online ISSN: 1521-3978

Associated Title(s): Annalen der Physik

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AdS/CFT correspondence · black holes · conformal fields · cosmology · d-branes · gauge fields · gravity · Lie algebras · noncommutative geometry · quantum entanglement · quantum field theories · quantum gravity · quantum groups · quantum information · quantum physics · qubits · standard model · string theories · supergravity · supersymmetry ·

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  1. Aspects of quadratic gravity (pages 176–189)

    Luis Alvarez-Gaume, Alex Kehagias, Costas Kounnas, Dieter Lüst and Antonio Riotto

    Article first published online: 10 FEB 2016 | DOI: 10.1002/prop.201500100

    The authors discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, the physical propagating modes in some specific backgrounds are analyzed in detail. After confirming that the pure R2 theory is indeed ghost free it is pointed out that for flat backgrounds the pure R2 theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence there is a subtle interplay between the UV and IR properties of higher order gravity. The corresponding Newton's law for general quadratic curvature theories is calculated and it is discussed how quadratic actions may be obtained from a fundamental theory like string- or M-theory. It is demonstrated that string theory on non-compact CY3 manifolds, like a line bundle over CP2, may indeed lead to gravity dynamics determined by a higher curvature action.

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    Entanglement entropy in a holographic Kondo model (pages 109–130)

    Johanna Erdmenger, Mario Flory, Carlos Hoyos, Max-Niklas Newrzella and Jackson M. S. Wu

    Article first published online: 18 JAN 2016 | DOI: 10.1002/prop.201500099

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    Entanglement and impurity entropies in a recent holographic model of a magnetic impurity interacting with a strongly coupled system are calculated. There is an RG flow to an IR fixed point where the impurity is screened, leading to a decrease in impurity degrees of freedom. This information loss corresponds to a volume decrease in our dual gravity model, which consists of a codimension one hypersurface embedded in a BTZ black hole background in three dimensions. There are matter fields defined on this hypersurface which are dual to Kondo field theory operators. In the large N limit, the formation of the Kondo cloud corresponds to the condensation of a scalar field. The entropy is calculated according to the Ryu-Takayanagi prescription. This requires to determine the backreaction of the hypersurface on the BTZ geometry, which is achieved by solving the Israel junction conditions. It is found that the larger the scalar condensate gets, the more the volume of constant time slices in the bulk is reduced, shortening the bulk geodesics and reducing the impurity entropy. This provides a new non-trivial example of an RG flow satisfying the g-theorem.

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    Addendum to computational complexity and black hole horizons (pages 44–48)

    Leonard Susskind

    Article first published online: 18 JAN 2016 | DOI: 10.1002/prop.201500093

    In this addendum to the previous paper two points are discussed. In the first additional evidence is provided for a dual connection between the geometric length of an Einstein-Rosen bridge and the computational complexity of the quantum state of the dual CFT's. The relation between growth of complexity and Page's “Extreme Cosmic Censorship" principle is also remarked on. The second point involves a gedanken experiment in which Alice measures a complete set of commuting observables at her end of an Einstein-Rosen bridge is discussed. An apparent paradox is resolved by appealing to the properties of GHZ tripartite entanglemen.

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    The typical-state paradox: diagnosing horizons with complexity (pages 84–91)

    Leonard Susskind

    Article first published online: 18 JAN 2016 | DOI: 10.1002/prop.201500091

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    The concept of transparent and opaque horizons is defined. One example of opaqueness is the presence of a firewall. Two apparently contradictory statements are reconciled: The overwhelming number of black hole states have opaque horizons; and: All black holes formed by natural processes have transparent horizons. A diagnostic is proposed for transparency, namely that the computational complexity of the state be increasing with time. It is shown that opaque horizons are extremely unstable and that the slightest perturbation will make them transparent within a scrambling time.

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    Computational complexity and black hole horizons (pages 24–43)

    Leonard Susskind

    Article first published online: 18 JAN 2016 | DOI: 10.1002/prop.201500092

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    Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find black holes that form in sudden collapse, and then evaporate. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity.

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