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Timelike and gravitational anomalous entanglement from the inner horizon
by Qiang Wen, Mingshuai Xu and Haocheng Zhong
Submission summary
| Authors (as registered SciPost users): | Qiang Wen · Haocheng Zhong |
| Submission information | |
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| Preprint Link: | scipost_202501_00011v1 (pdf) |
| Date submitted: | 2025-01-09 09:14 |
| Submitted by: | Wen, Qiang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In the context of the AdS$_3$/CFT$_2$, the boundary causal development and the entanglement wedge of any boundary spacelike interval can be mapped to a thermal CFT$_2$ and a Rindler $\widetilde{\text{AdS}_3}$ respectively via certain boundary and bulk Rindler transformations. Nevertheless, the Rindler mapping is not confined in the entanglement wedges. While the outer horizon of the Rindler $\widetilde{\text{AdS}_3}$ is mapped to the RT surface, we also identify the pre-image of the inner horizon in the original AdS$_3$, which we call the inner RT surface. In this paper we give some new physical interpretation for the inner RT surface. First, the inner RT surface breaks into two pieces which anchor on the two tips of the causal development. Furthermore, we can take the two tips as the endpoints of a certain timelike interval and the inner RT surface is exactly the spacelike geodesic that represents the real part of the so-called holographic timelike entanglement entropy (HTEE). We also identify a timelike geodesic at boundary of the extended entanglement wedge, which represents the imaginary part of the HTEE. Second, in the duality between the topological massive gravity (TMG) and gravitational anomalous CFT$_2$, the entanglement entropy and the mixed state correlation that is dual to the entanglement wedge cross section (EWCS) receive correction from the Chern-Simons term in the TMG. We find that, the correction to the holographic entanglement entropy can be reproduced by the area of the inner RT surface with a proper regulation, while the mixed state correlation can be represented by the saddle geodesic chord connecting the two pieces of the inner RT surface of the mixed state we consider, which we call the inner EWCS. The equivalence between the twist on the RT surface and the length of inner RT surface is also discussed.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1. Novel Insights: The manuscript offers a fresh perspective on holographic entanglement entropy by introducing the inner RT surface (IRT surface) and investigating its role in gravitational anomalies.
2.Clear Structure: The paper is well-organized, with topics clearly separated and ideas logically progressing. The modular slices, PEE, and gravitational anomalous corrections sections are particularly detailed and accessible.
3. Connection to Previous Work: The authors effectively build upon previous studies in holographic entanglement, particularly regarding the EWCS and holographic entanglement entropy in TMG. The integration of gravitational anomalies into the entanglement framework is valuable.
Weaknesses
1. The manuscript occasionally presents complex mathematical derivations without sufficient explanation, which could make it difficult for readers unfamiliar with the specific methods employed (e.g., worldline actions, regulated geodesic chords, etc.).
Recommendation: Provide more detailed explanations for key steps in the mathematical derivations, especially in the sections involving the IRT surface and the replica trick.
2. Discussing the mixed state correlation and its connection to the IRT surface is interesting but could benefit from a broader generalization. Including a more comprehensive analysis of how these results extend to other non-AdS geometries or more general holographic setups would be helpful.
Recommendation: Consider discussing the potential generalization of the IRT surface and its relevance to more generic holographic models.
3. The physical interpretation of the inner RT surface (IRT surface) and its connection to timelike entanglement entropy is not immediately intuitive. While the authors explain the concept clearly in technical terms, a more accessible explanation for a broader audience might be helpful.
Recommendation: A more intuitive explanation of the significance of the IRT surface, perhaps with more physical analogies, would make the results more accessible.
Specific Questions/Concerns:
What is the physical motivation for choosing the inner RT surface over other possible surfaces, particularly in the context of gravitational anomalies?
Could you provide a more detailed explanation of how the timelike entanglement entropy is related to the imaginary part of the holographic entanglement entropy and the role of the inner RT surface in this context?
The paper mentions correcting the holographic entanglement entropy due to the Chern-Simons term. How general is this result? Does it hold for all gravitational anomalies, or is it specific to certain anomalies?
How does the proposed framework for mixed-state correlations (inner EWCS) compare with other methods for dealing with mixed-state holography, such as the swing surface or the island prescription?
Report
This paper contributes to the study of holographic entanglement entropy in gravitational anomalies. The introduction of the inner RT surface provides new insights into the holographic description of mixed-state entanglement. However, some sections could benefit from more precise explanations and further elaboration, particularly in the mathematical and physical interpretation of the results. I recommend acceptance of the manuscript after these revisions.
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