TY - JOUR

T1 - A canonical purification for the entanglement wedge cross-section

AU - Dutta, Souvik

AU - Faulkner, Thomas

N1 - Publisher Copyright:
© 2021, The Author(s).

PY - 2021/3

Y1 - 2021/3

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Conformal Field Theory

KW - Renormalization Group

UR - http://www.scopus.com/inward/record.url?scp=85103351066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85103351066&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2021)178

DO - 10.1007/JHEP03(2021)178

M3 - Article

AN - SCOPUS:85103351066

SN - 1126-6708

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 3

M1 - 178

ER -