Notes on entanglement wedge cross sections

Abstract

We consider the holographic candidate for the entanglement of purification $E_P$, given by the minimal cross sectional area of an entanglement wedge $E_W$. The $E_P$ is generally very complicated quantity to obtain in field theories, thus to establish the conjectured relationship one needs to test if $E_W$ and $E_P$ share common features. In this paper the entangling regions we consider are slabs, concentric spheres, and creases in field theories in Minkowski space. The latter two can be mapped to regions in field theories defined on spheres, thus corresponding to entangled caps and orange slices, respectively. We work in general dimensions and for slabs we also consider field theories at finite temperature and confining theories. We find that $E_W$, similarly to holographic mutual information, is not a monotonic function of a scale. We also study a full ten-dimensional string theory geometry dual to a non-trivial RG flow of a three-dimensional Chern-Simons matter theory coupled to fundamentals. We show that also in this case $E_W$ behaves non-trivially, which if connected to $E_P$, lends further support that the system can undergo purification simply by expansion or reduction in scale.

33 pages, 11 figures, a typo corrected, refs added

References in corpus (15)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Entanglement as a Probe of Confinement
• Universality of corner entanglement in conformal field theories
• Entanglement Wedge Cross Section from the Dual Density Matrix
• Geometric Aspects of Holographic Bit Threads
• Holographic Entanglement of Purification from Conformal Field Theories
• Some Aspects of Entanglement Wedge Cross-Section
• Confinement, Phase Transitions and non-Locality in the Entanglement Entropy
• On shape dependence of holographic mutual information in AdS4
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Holographic Entanglement Entropy of Multiple Strips
• Holographic entanglement of purification for thermofield double states and thermal quench
• Entanglement of Purification and Multiboundary Wormhole Geometries
• Gravity dual of a multilayer system
• Information flows in strongly coupled ABJM theory

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