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

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

Resultado de la investigación: Article

5 Citas (Scopus)

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
N.º10
DOI
EstadoPublished - 13 mar 2015

Huella dactilar

Rényi Entropy
Q-analogue
Lobachevskian geometry
Entropy
entropy
analogs
Entanglement
Anomaly
Trace
AdS/CFT
Conformal Mapping
Hyperbolic Space
Spinor
hyperbolic coordinates
anomalies
Determinant
Logarithmic
Defects
Conformal mapping
Scalar

ASJC Scopus subject areas

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

Citar esto

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AU - Diaz, D. E.

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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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