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arXiv · 1408.1931

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

R. Aros·F. Bugini·D. E. Diaz
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Abstract

We describe a holographic approach to explicitly compute 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 map 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 resulting functional determinant. We explicitly verify the connection with the type-A trace anomaly for the entanglement entropy, whereas the Renyi entropy is computed with aid of the Sommerfeld formula in order to deal with a conical defect. As a by-product, we show that 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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R. Aros, F. Bugini, D. E. Diaz. 2014-08-08. On Renyi entropy for free conformal fields: holographic and q-analog recipes. https://doi.org/10.1088/1751-8113/48/10/105401

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