Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-07-09
J.Stat.Mech.0801:P01012,2008
Physics
High Energy Physics
High Energy Physics - Theory
7 pages, minor changes
Scientific paper
10.1088/1742-5468/2008/01/P01012
The trace of integer powers of the local density matrix corresponding to the vacuum state reduced to a region V can be formally expressed in terms of a functional integral on a manifold with conical singularities. Recently, some progress has been made in explicitly evaluating this type of integrals for free fields. However, finding the associated geometric entropy remained in general a difficult task involving an analytic continuation in the conical angle. In this paper, we obtain this analytic continuation explicitly exploiting a relation between the functional integral formulas and the Chung-Peschel expressions for the density matrix in terms of correlators. The result is that the entropy is given in terms of a functional integral in flat Euclidean space with a cut on V where a specific boundary condition is imposed. As an example we get the exact entanglement entropies for massive scalar and Dirac free fields in 1+1 dimensions in terms of the solutions of a non linear differential equation of the Painleve V type.
Casini Horacio
Huerta Marcos
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