Universal terms for the entanglement entropy in 2+1 dimensions

被引：164

作者：

Casini, H. ^{[1
]}

Huerta, M. ^{[1
]}

机构：

[1] Ctr Atom Bariloche, RA-8400 San Carlos De Bariloche, Rio Negro, Argentina

来源：

NUCLEAR PHYSICS B | 2007年 / 764卷 / 03期

关键词：

entanglement entropy; conformal anomaly; three-dimensional field theory;

D O I：

10.1016/j.nuclphysb.2006.12.012

中图分类号：

O412 [相对论、场论]; O572.2 [粒子物理学];

学科分类号：

摘要：

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. (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：183 / 201

页数：19

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