Abstract
We study the holographic entanglement entropy of spatial regions with corners in the AdS4/BCFT3 correspondence by considering three dimensional boundary conformal field theories whose boundary is a timelike plane. We compute analytically the corner function corresponding to an infinite wedge having one edge on the boundary. A relation between this corner function and the holographic one point function of the stress tensor is observed. An analytic expression for the corner function of an infinite wedge having only its tip on the boundary is also provided. This formula requires to find the global minimum among two extrema of the area functional. The corresponding critical configurations of corners are studied. The results have been checked against a numerical analysis performed by computing the area of the minimal surfaces anchored to some finite domains containing corners.
Highlights
Entanglement entropy has been largely studied during the last two decades in quantum field theory, quantum gravity, quantum many-body systems and quantum information
We study the holographic entanglement entropy of spatial regions with corners in the AdS4/BCFT3 correspondence by considering three dimensional boundary conformal field theories whose boundary is a timelike plane
Focussing on the case of AdS4/BCFT3, we find it worth anticipating that for the domains A in the z = 0 half plane considered in the following, we find that the corresponding minimal surfaces γA are part of auxiliary minimal surfaces γA,aux ⊂ H3 anchored to the boundary of suitable auxiliary domains A aux ⊂ R2 = ∂H3
Summary
Entanglement entropy has been largely studied during the last two decades in quantum field theory, quantum gravity, quantum many-body systems and quantum information (see [1,2,3,4] for reviews). One can consider a more general class of domains A whose boundaries contain vertices of the types introduced above which have x > 0 In these cases the area law term of the entanglement entropy is like the one in (1.4) and the coefficient of the logarithmic divergence is the sum of (1.3) and (1.5). In this manuscript we are interested in the corner functions occurring in (1.5) for a BCFT3 at strong coupling. All the computational details underlying their derivations and some generalisations to an arbitrary number of spacetime dimensions have been collected and discussed in the appendices A, B, C, D, E, F, G and H
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