Entanglement entropy for the n-sphere

Details Entanglement entropy for the n-sphere Entanglement entropy for the n-sphere

2010-07-12

arxiv.org/abs/1007.1813v2

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, no figures, references added

Scientific paper

We calculate the entanglement entropy for a sphere and a massless scalar field in any dimensions. The reduced density matrix is expressed in terms of the infinitesimal generator of conformal transformations keeping the sphere fixed. The problem is mapped to the one of a thermal gas in a hyperbolic space and solved by the heat kernel approach. The coefficient of the logarithmic term in the entropy for 2 and 4 spacetime dimensions are in accordance with previous numerical and analytical results. In particular, the four dimensional result, together with the one reported by Solodukhin, gives support to the Ryu-Takayanagi holographic anzats. We also find there is no logarithmic contribution to the entropy for odd space time dimensions.

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