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

R Aros, F Bugini, D E Díaz
2015 Journal of Physics A: Mathematical and Theoretical  
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
more » ... o 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.
doi:10.1088/1751-8113/48/10/105401 fatcat:ntfq27egazbmffuybuqp7nkpya