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Multi-entropy at low Renyi index in 2d CFTs
by Jonathan Harper, Tadashi Takayanagi, Takashi Tsuda
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Jonathan Harper |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2401.04236v3 (pdf) |
| Date accepted: | 2024-05-02 |
| Date submitted: | 2024-04-10 05:08 |
| Submitted by: | Harper, Jonathan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
For a static time slice of AdS$_3$ we describe a particular class of minimal surfaces which form trivalent networks of geodesics. Through geometric arguments we provide evidence that these surfaces describe a measure of multipartite entanglement. By relating these surfaces to Ryu-Takayanagi surfaces it can be shown that this multipartite contribution is related to the angles of intersection of the bulk geodesics. A proposed boundary dual, the multi-entropy, generalizes replica trick calculations involving twist operators by considering monodromies with finite group symmetry beyond the cyclic group used for the computation of entanglement entropy. We make progress by providing explicit calculations of Renyi multi-entropy in two dimensional CFTs and geometric descriptions of the replica surfaces for several cases with low genus. We also explore aspects of the free fermion and free scalar CFTs. For the free fermion CFT we examine subtleties in the definition of the twist operators used for the calculation of Renyi multi-entropy. In particular the standard bosonization procedure used for the calculation of the usual entanglement entropy fails and a different treatment is required.
Author comments upon resubmission
List of changes
1. Added a new section 2.1 defining general multi-trace measures for a finite group, providing notation, and a more complete description along with basic examples.
a. Better emphasized that the measure depends on a choice of group element for each party of the state.
b. More clearly stated that the group representation for a group of order $n$ should be chosen to be the regular action on $n$ points.
2. Minor changes were made to section 2.2:
a. Better highlighted the relation between the definition of multi-trace measures and the corresponding construction in the 2d CFT using replica copies.
b. Emphasized that the multi-entropy is an example of a specific multi-trace measure where the group elements for each party are chosen appropriately from a particular direct product of cyclic groups.
3. All of the notional and changes have been implemented. Specifically :
a. Switched to common convention of group order being listed as a subscript.
b. Corrected tensor products to cartesian products.
c. For the multi-trace measures (see above) changed notation such that the tensor indices of the density matrix are more intuitive: For party $A_i $ the index for the ket and bra is label $a_i $ and $a'_i$ respectively.
4. All of the mentioned typos have been corrected.
Published as SciPost Phys. 16, 125 (2024)
Reports on this Submission
Report #1 by Matthew Headrick (Referee 1) on 2024-4-19 (Invited Report)
Report
Yes, the journal's acceptance criteria are met. The new version adequately addresses the minor presentational issues identified in the previous referee reports.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)