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Analytic results on the geometric entropy for free fields · Around

2007

Analytic results on the geometric entropy for free fields

Casini, H., Huerta, M.

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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.

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