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

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.

9 pages

References in corpus (7)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Entanglement entropy for even spheres
• Entanglement entropy of round spheres
• Renyi Entropy and Geometry
• Determinants and conformal anomalies of GJMS operators on spheres