Universal terms for the entanglement entropy in 2+1 dimensions

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dc.creatorCasini, H.
dc.creatorHuerta, M.
dc.date2006-06-27
dc.date2006-11-28
dc.date.accessioned2026-07-07T10:25:58Z
dc.date.available2026-07-07T10:25:58Z
dc.descriptionWe 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.
dc.description15 pages, 3 figures, extended version with full calculations, added references
dc.identifierhttps://arxiv.org/abs/hep-th/0606256
dc.identifierhttp://arxiv.org/abs/hep-th/0606256
dc.identifierNucl.Phys.B764:183-201,2007
dc.identifierdoi:10.1016/j.nuclphysb.2006.12.012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/176724
dc.subjectHigh Energy Physics - Theory
dc.subjectOther Condensed Matter
dc.subjectQuantum Physics
dc.titleUniversal terms for the entanglement entropy in 2+1 dimensions
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