Entanglement entropy for even spheres
Abstract
The coefficient of the logarithmic term in the entropy on even spheres is re-computed by the local technique of integrating the finite temperature energy density up to the horizon on static d--dimensional de Sitter space and thence finding the entropy by thermodynamics. Numeric evaluation yields the known answer i.e. (minus) the conformal anomaly on the d-sphere. The de Sitter quantities are obtained by conformal transformation of the Rindler ones, themselves obtained, for convenience, from those around a cosmic string. The expressions are given in terms of generalised Bernoulli polynomials for which an identity is derived. The arising spherical conformal anomaly is discussed and a formula is given for it for Branson's higher GJMS Laplacian, P_2k, as an oscillating polynomial in the level, k.
Cite
@article{arxiv.1009.3854,
title = {Entanglement entropy for even spheres},
author = {J. S. Dowker},
journal= {arXiv preprint arXiv:1009.3854},
year = {2010}
}
Comments
11 pages. Minor corrections. Extended discussion of conformal anomaly on spheres including that for GJMS operators. References added