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A canonical purification for the entanglement wedge cross-section

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]
  1. Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics; Univ. of Illinois at Urbana-Champaign, IL (United States)
  2. Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics
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In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy. From the bulk point of view, we show that half the area of the reflected minimal surface gives a reinterpretation of the notion of the entanglement wedge cross-section. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an explicit holographic construction of the canonical purification, introduced by Engelhardt and Wall; the reflected minimal surfaces are simply RT surfaces in this new spacetime. We contrast our results with the entanglement of purification conjecture, and finally comment on the continuum limit where we find a relation to the split property: the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor introduced by Doplicher and Longo.
Research Organization:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0019183
OSTI ID:
1852920
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 3 Vol. 2021; ISSN 1029-8479
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AdS-CFT Correspondence
Conformal Field Theory
Physics
Renormalization Group