On Renyi entropy for free conformal fields: Holographic and q-analog recipes

R. Aros, F. Bugini, D. E. Diaz

Resultado de la investigación: Contribución a la publicaciónArticle

  • 1 Citas

Resumen

We describe a holographic approach to explicitly computing the universal logarithmic contributions to entanglement and Renyi entropies for free conformal scalar and spinor fields on even-dimensional spheres. This holographic derivation proceeds in two steps: first, following Casini and Huerta, a conformal mapping to thermal entropy in a hyperbolic geometry; then identification of the hyperbolic geometry with the conformal boundary of a bulk hyperbolic space and use of an AdS/CFT holographic formula to compute the resultant functional determinant. We explicitly verify the connection with the type-A trace anomaly for the entanglement entropy, whereas the Renyi entropy is computed with the aid of the Sommerfeld formula in order to deal with a conical defect. We show that as a by-product, the log coefficient of the Renyi entropy for round spheres can be efficiently obtained as the q-analog of a procedure similar to the one found by Cappelli and D'Appollonio that rendered the type-A trace anomaly.

Idioma originalEnglish
Número de artículo105401
PublicaciónJournal of Physics A: Mathematical and Theoretical
Volumen48
Número de edición10
Identificadores de objetos digitales
EstadoPublished - 13 mar 2015

Huella dactilar

Entropy
Geometry
Conformal mapping
Byproducts
Defects

Keywords

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Modelling and Simulation
    • Mathematical Physics
    • Physics and Astronomy(all)

    Citar esto

    Aros, R.; Bugini, F.; Diaz, D. E. / On Renyi entropy for free conformal fields : Holographic and q-analog recipes.

    En: Journal of Physics A: Mathematical and Theoretical, Vol. 48, N.º 10, 105401, 13.03.2015.

    Resultado de la investigación: Contribución a la publicaciónArticle

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    abstract = "We describe a holographic approach to explicitly computing the universal logarithmic contributions to entanglement and Renyi entropies for free conformal scalar and spinor fields on even-dimensional spheres. This holographic derivation proceeds in two steps: first, following Casini and Huerta, a conformal mapping to thermal entropy in a hyperbolic geometry; then identification of the hyperbolic geometry with the conformal boundary of a bulk hyperbolic space and use of an AdS/CFT holographic formula to compute the resultant functional determinant. We explicitly verify the connection with the type-A trace anomaly for the entanglement entropy, whereas the Renyi entropy is computed with the aid of the Sommerfeld formula in order to deal with a conical defect. We show that as a by-product, the log coefficient of the Renyi entropy for round spheres can be efficiently obtained as the q-analog of a procedure similar to the one found by Cappelli and D'Appollonio that rendered the type-A trace anomaly.",
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    On Renyi entropy for free conformal fields : Holographic and q-analog recipes. / Aros, R.; Bugini, F.; Diaz, D. E.

    En: Journal of Physics A: Mathematical and Theoretical, Vol. 48, N.º 10, 105401, 13.03.2015.

    Resultado de la investigación: Contribución a la publicaciónArticle

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    T2 - Journal of Physics A: Mathematical and Theoretical

    AU - Aros,R.

    AU - Bugini,F.

    AU - Diaz,D. E.

    PY - 2015/3/13

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    N2 - We describe a holographic approach to explicitly computing the universal logarithmic contributions to entanglement and Renyi entropies for free conformal scalar and spinor fields on even-dimensional spheres. This holographic derivation proceeds in two steps: first, following Casini and Huerta, a conformal mapping to thermal entropy in a hyperbolic geometry; then identification of the hyperbolic geometry with the conformal boundary of a bulk hyperbolic space and use of an AdS/CFT holographic formula to compute the resultant functional determinant. We explicitly verify the connection with the type-A trace anomaly for the entanglement entropy, whereas the Renyi entropy is computed with the aid of the Sommerfeld formula in order to deal with a conical defect. We show that as a by-product, the log coefficient of the Renyi entropy for round spheres can be efficiently obtained as the q-analog of a procedure similar to the one found by Cappelli and D'Appollonio that rendered the type-A trace anomaly.

    AB - We describe a holographic approach to explicitly computing the universal logarithmic contributions to entanglement and Renyi entropies for free conformal scalar and spinor fields on even-dimensional spheres. This holographic derivation proceeds in two steps: first, following Casini and Huerta, a conformal mapping to thermal entropy in a hyperbolic geometry; then identification of the hyperbolic geometry with the conformal boundary of a bulk hyperbolic space and use of an AdS/CFT holographic formula to compute the resultant functional determinant. We explicitly verify the connection with the type-A trace anomaly for the entanglement entropy, whereas the Renyi entropy is computed with the aid of the Sommerfeld formula in order to deal with a conical defect. We show that as a by-product, the log coefficient of the Renyi entropy for round spheres can be efficiently obtained as the q-analog of a procedure similar to the one found by Cappelli and D'Appollonio that rendered the type-A trace anomaly.

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