Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-06-27
Nucl.Phys.B764:183-201,2007
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, 3 figures, extended version with full calculations, added references
Scientific paper
10.1016/j.nuclphysb.2006.12.012
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.
Casini Horacio
Huerta Marcos
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