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

TL;DR

This paper presents a holographic method to compute universal logarithmic contributions to entanglement and Renyi entropies for free conformal fields on spheres, linking them to trace anomalies and q-analog procedures.

Contribution

It introduces a holographic approach combining conformal mapping and AdS/CFT techniques to explicitly calculate entanglement and Renyi entropy coefficients for free conformal fields.

Findings

Verified connection between entanglement entropy and type-A trace anomaly.

Derived Renyi entropy using Sommerfeld formula for conical defects.

Showed Renyi entropy's log-coefficient as a q-analog of trace anomaly procedures.

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.