Analytic results on the geometric entropy for free fields

CASINI, HORACIO; HUERTA, MARINA

JSTAT

IOP

Año: 2008 vol. P010 p. 1 - 9

1742-5468

The trace of integer powers of the local density matrix ho_V 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 ho_V 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 Painlev´e V type.