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Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies

by Qiang Wen and Haocheng Zhong

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Submission summary

Authors (as registered SciPost users): Qiang Wen · Haocheng Zhong
Submission information
Preprint Link: scipost_202206_00003v2  (pdf)
Date accepted: 2022-07-26
Date submitted: 2022-07-23 12:36
Submitted by: Wen, Qiang
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


The balanced partial entanglement (BPE) was observed to give the reflected entropy and the entanglement wedge cross-section (EWCS) for various mixed states in different theories \cite{Wen:2021qgx,Camargo:2022mme}. It can be calculated in different purifications, and is conjectured to be independent from purifications. In this paper we calculate the BPE and the EWCS in generic covariant scenarios in two-dimensional CFTs with and without gravitational anomalies, and find that they coincide with the reflected entropy. In covariant configurations we determine the partition for the purifying system with the help of the gravitational anomalies, and we extend our discussion to topological massive gravity (TMG). We give the first prescription to evaluate the entropy quantity associated to the EWCS beyond Einstein gravity, i.e. the correction to the EWCS from the Chern-Simons term in TMG. Apart from the gravity theory and geometry, further input from the mixed state should be taken into account.

List of changes

The main changes are in the following

1, we added a figure at the end of section 3 to give an example to numerically test that the crossing PEE arrives its the minimal value at the balanced point.

2, a paragraph is added at the end of section 5.1 to briefly discuss the relations of the BPE and EWCS with the negativity.

Also there are multiple minor changes according to the request changes from the referee.

Published as SciPost Phys. 13, 056 (2022)

Reports on this Submission

Anonymous Report 1 on 2022-7-24 (Invited Report)


I thank the authors for having addressed all the points raised in the report. I recommend this manuscript for publication on SciPost.

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