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arXiv · 1212.2098

Sphere Renyi entropies

J. S. Dowker
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Abstract

I give some scalar field theory calculations on a d-dimensional lune of arbitrary angle, evaluating, numerically, the effective action which is expressed as a simple quadrature, for conformal coupling. Using this, the entanglement and Renyi entropies are computed. Massive fields are also considered and a renormalisation to make the (one-loop) effective action vanish for infinite mass is suggested and used, not entirely successfully. However a universal coefficient is derived from the large mass expansion. From the deformation of the corresponding lune result, I conjecture that the effective action on all manifolds with a simple conical singularity has an extremum when the singularity disappears. For the round sphere, I show how to convert the quadrature form of the conformal Laplacian determinant into the more usual sum of Riemann zeta functions (and log2).

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J. S. Dowker. 2013-02-11. Sphere Renyi entropies. https://doi.org/10.1088/1751-8113%2F46%2F22%2F225401

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