Abstract
We study corner contributions to holographic mutual information for entangling regions composed of a set of disjoint sectors of a single infinite circle in three-dimensional conformal field theories. In spite of the UV divergence of holographic mutual information, it exhibits a first order phase transition. We show that tripartite information is also divergent for disjoint sectors, which is in contrast with the well-known feature of tripartite information being finite even when entangling regions share boundaries. We also verify the locality of corner effects by studying mutual information between regions separated by a sharp annular region. Possible extensions to higher dimensions and hyperscaling violating geometries is also considered for disjoint sectors.
Highlights
Entanglement entropy in QFTs is a UV-divergent quantity which its leading divergence is proportional to the area of the entangling region V, due to the leading contribution of the near-boundary local degrees of freedom i.e. [1, 3, 9]
We study corner contributions to holographic mutual information for entangling regions composed of a set of disjoint sectors of a single infinite circle in 3-dimensional conformal field theories
We have considered two different kinds of singular geometries i.e. a set of disjoint sectors of a single infinite circle which have a contact point and two sharp concentric circles which are completely disjoint
Summary
In this subsection we study the holographic mutual information for the specific configuration mentioned above. In the left plot the contributions of connected and disconnected configurations to the universal part of HEE for a fixed opening angle are compared These quantities are defined as follows adis. In order to investigate the behavior of HMI in this singular configuration more generally, we consider the case where the opening angles of the entangling regions are not equal, i.e., Ω1 = Ω2. These plots show the transition points of this quantity and regions with non-vanishing HMI
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