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Holographic Renyi entropy of 2d CFT in KdV generalized ensemble

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Title: Holographic Renyi entropy of 2d CFT in KdV generalized ensemble
Authors: Liangyu Chen, Anatoly Dymarsky, Jia Tian, Huajia Wang
Source: Journal of High Energy Physics, Vol 2025, Iss 1, Pp 1-50 (2025)
Publisher Information: SpringerOpen, 2025.
Publication Year: 2025
Collection: LCC:Nuclear and particle physics. Atomic energy. Radioactivity
Subject Terms: AdS-CFT Correspondence, Conformal and W Symmetry, Holography and Condensed Matter Physics (AdS/CMT), Black Holes, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
More Details: Abstract The eigenstate thermalization hypothesis (ETH) in chaotic two dimensional CFTs is subtle due to infinitely many conserved KdV charges. Previous works have demonstrated that primary CFT eigenstates have flat entanglement spectrum, which is very different from the microcanonical ensemble. This result is an apparent contradiction to conventional ETH, which does not take KdV charges into account. In a companion paper [1], we resolve this discrepancy by studying the subsystem entropy of a chaotic CFT in KdV-generalized Gibbs and microcanonical ensembles. In this paper, we carry out parallel computations in the context of AdS/CFT. We focus on the high density limit, which is equivalent to thermodynamic limit in conformal theories. In this limit holographic Renyi entropy can be computed using the so-called gluing construction. We explicitly study the KdV-generalized microcanonical ensemble with the densities of the first two KdV charges Q 1 $$ \left\langle {\mathcal{Q}}_1\right\rangle $$ = q 1, Q 3 $$ \left\langle {\mathcal{Q}}_3\right\rangle $$ = q 3 fixed and obeying q 3 − q 1 2 ≪ q 1 2 $$ {q}_1^2\ll {q}_1^2 $$ . In this regime we found that the refined Renyi entropy S ~ n $$ {\overset{\sim }{S}}_n $$ is n-independent for n > n cut, where n cut depends on q 1, q 3. By taking the primary state limit q 3 → q 1 2 $$ {q}_1^2 $$ , we recover flat entanglement spectrum characteristic of fixed-area states, in agreement with the primary state behavior. This provides a consistency check of the KdV-generalized ETH in 2d CFTs.
Document Type: article
File Description: electronic resource
Language: English
ISSN: 1029-8479
Relation: https://doaj.org/toc/1029-8479
DOI: 10.1007/JHEP01(2025)067
Access URL: https://doaj.org/article/2c65064d609542a49715e92536c47a1a
Accession Number: edsdoj.2c65064d609542a49715e92536c47a1a
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  Data: Abstract The eigenstate thermalization hypothesis (ETH) in chaotic two dimensional CFTs is subtle due to infinitely many conserved KdV charges. Previous works have demonstrated that primary CFT eigenstates have flat entanglement spectrum, which is very different from the microcanonical ensemble. This result is an apparent contradiction to conventional ETH, which does not take KdV charges into account. In a companion paper [1], we resolve this discrepancy by studying the subsystem entropy of a chaotic CFT in KdV-generalized Gibbs and microcanonical ensembles. In this paper, we carry out parallel computations in the context of AdS/CFT. We focus on the high density limit, which is equivalent to thermodynamic limit in conformal theories. In this limit holographic Renyi entropy can be computed using the so-called gluing construction. We explicitly study the KdV-generalized microcanonical ensemble with the densities of the first two KdV charges Q 1 $$ \left\langle {\mathcal{Q}}_1\right\rangle $$ = q 1, Q 3 $$ \left\langle {\mathcal{Q}}_3\right\rangle $$ = q 3 fixed and obeying q 3 − q 1 2 ≪ q 1 2 $$ {q}_1^2\ll {q}_1^2 $$ . In this regime we found that the refined Renyi entropy S ~ n $$ {\overset{\sim }{S}}_n $$ is n-independent for n > n cut, where n cut depends on q 1, q 3. By taking the primary state limit q 3 → q 1 2 $$ {q}_1^2 $$ , we recover flat entanglement spectrum characteristic of fixed-area states, in agreement with the primary state behavior. This provides a consistency check of the KdV-generalized ETH in 2d CFTs.
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        Type: general
      – SubjectFull: Conformal and W Symmetry
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      – TitleFull: Holographic Renyi entropy of 2d CFT in KdV generalized ensemble
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