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**1 - 5**of**5**### On shape dependence of holographic mutual information in AdS4

, 2014

"... We study the holographic mutual information in AdS4 of disjoint spatial domains in the boundary which are delimited by smooth closed curves. A numerical method which approximates a local minimum of the area functional through triangulated surfaces is employed. After some checks of the method against ..."

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We study the holographic mutual information in AdS4 of disjoint spatial domains in the boundary which are delimited by smooth closed curves. A numerical method which approximates a local minimum of the area functional through triangulated surfaces is employed. After some checks of the method against existing analytic results for the holographic entanglement entropy, we compute the holographic mutual information of equal domains delimited by ellipses, superellipses or the boundaries of two dimensional spherocylinders, finding also the corresponding transition curves along which the holographic mutual information vanishes.

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, 2010

"... This paper was prepared based on the information available at the time it was completed on April 27, 2010. The views expressed in this document are those of the staff team and do not necessarily reflect the views of the government of Albania or the Executive Board of the IMF. The policy of publicati ..."

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This paper was prepared based on the information available at the time it was completed on April 27, 2010. The views expressed in this document are those of the staff team and do not necessarily reflect the views of the government of Albania or the Executive Board of the IMF. The policy of publication of staff reports and other documents by the IMF allows for the deletion of market-sensitive information.

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, 2014

"... In this paper we extend and simplify previous results regarding the computation of Euclidean Wilson loops in the context of the AdS/CFT correspondence, or, equivalently, the problem of finding minimal area surfaces in hyperbolic space (Euclidean AdS3). If the Wilson loop is given by a boundary curve ..."

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In this paper we extend and simplify previous results regarding the computation of Euclidean Wilson loops in the context of the AdS/CFT correspondence, or, equivalently, the problem of finding minimal area surfaces in hyperbolic space (Euclidean AdS3). If the Wilson loop is given by a boundary curve ~X(s) we define, using the integrable properties of the system, a family of curves ~X(λ, s) depending on a complex parameter λ known as the spectral parameter. This family has remarkable properties. As a function of λ, ~X(λ, s) has cuts and therefore is appropriately defined on a hyperelliptic Riemann surface, namely it determines the spectral curve of the problem. Moreover, ~X(λ, s) has an essential singularity at the origin λ = 0. The coeffi-cients of the expansion of ~X(λ, s) around λ = 0, when appropriately