Universal terms for the entanglement entropy in 2+1 dimensions

H. Casini; M. Huerta

doi:10.1016/j.nuclphysb.2006.12.012

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arXiv · hep-th/0606256

Universal terms for the entanglement entropy in 2+1 dimensions

H. Casini·M. Huerta

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Abstract

We show that the entanglement entropy and alpha entropies corresponding to spatial polygonal sets in $(2+1)$ dimensions contain a term which scales logarithmically with the cutoff. Its coefficient is a universal quantity consisting in a sum of contributions from the individual vertices. For a free scalar field this contribution is given by the trace anomaly in a three dimensional space with conical singularities located on the boundary of a plane angular sector. We find its analytic expression as a function of the angle. This is given in terms of the solution of a set of non linear ordinary differential equations. For general free fields, we also find the small-angle limit of the logarithmic coefficient, which is related to the two dimensional entropic c-functions. The calculation involves a reduction to a two dimensional problem, and as a byproduct, we obtain the trace of the Green function for a massive scalar field in a sphere where boundary conditions are specified on a segment of a great circle. This also gives the exact expression for the entropies for a scalar field in a two dimensional de Sitter space.

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H. Casini, M. Huerta. 2006-11-28. Universal terms for the entanglement entropy in 2+1 dimensions. https://doi.org/10.1016/j.nuclphysb.2006.12.012

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