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Multi-entropy at low Renyi index in 2d CFTs

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arxiv 2401.04236 v3 pith:DQU3IAZX submitted 2024-01-08 hep-th

Jonathan Harper , Tadashi Takayanagi , Takashi Tsuda This is my paper · ORCID
classification hep-th
keywords surfacesmulti-entropycftsentanglementfreerenyiusedcalculation
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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.

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Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Multi-entropy and the Dihedral Measures at Quantum Critical Points

    hep-th 2025-06 conditional novelty 7.0 of 10

    The multi-entropy excess κ_2^(3) vanishes for the massless free scalar CFT, an exception to the general c/4 log 2 result, while the Ising model matches it, and new n=3 and n=4 values are proposed for the scalar theory.

  2. Holographic multipartite entanglement dynamics in AdS$_3$-Vaidya

    hep-th 2026-08 conditional novelty 6.0 of 10

    During a holographic global quench, multipartite entanglement's spatial range first expands then contracts, with higher-party entanglement relaxing later, while some tripartite signals persist or return to vacuum values.

  3. Notes on the Graph-Encoded Manifolds for the (Genuine) Multi-Entropy

    hep-th 2026-08 accept novelty 6.0 of 10

    For q=4 multi-entropy, every vertex link of the contraction graph has Euler characteristic n(3-n), so the graph encodes a smooth 3-manifold exactly at n=2 and develops conical singularities for all n≥3.

  4. The Entanglement Wedge Polygon

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    The paper defines the entanglement wedge polygon as the intersection of entanglement wedges external to individual homology regions and studies its topological and geometric properties in AdS examples.

  5. Black hole as a multipartite entangler: multi-entropy in AdS${}_3$/CFT${}_2$

    hep-th 2025-12 conditional novelty 6.0 of 10

    In pure BTZ black-hole states the genuine tripartite multi-entropy grows linearly with subsystem size at high temperature (volume law), peaks at (1/6) of the Bekenstein-Hawking entropy plus a universal constant, and c...

  6. Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy

    hep-th 2025-10 conditional novelty 6.0 of 10

    A generalized latent-entropy measure orders k-uniform states, maxes out on AME states, shows odd-party random states saturate it, and distinguishes SYK variants.

  7. More on genuine multi-entropy and holography

    hep-th 2025-04 conditional novelty 6.0 of 10

    A partition-number-based prescription constructs genuine multi-entropy with p(q)-p(q-1)-1 free parameters for any q, and AdS3 computations give nonzero O(1/G_N) values for q=3,4,5.

  8. Genuine multi-entropy and holography

    hep-th 2025-02 conditional novelty 6.0 of 10

    A new 'genuine multi-entropy' separates true q-party entanglement from lower-party pieces, and holographic systems are shown to carry O(1/G_N) genuine multipartite entanglement for connected regions.

  9. A New Genuine Multipartite Entanglement Measure: from Qubits to Multiboundary Wormholes

    hep-th 2024-11 conditional novelty 6.0 of 10

    L-entropy is a proposed genuine multipartite entanglement measure, maximal for GHZ states and 2-uniform states, with applications to random states and multiboundary wormholes.

  10. Emergent Holographic Spacetime from Quantum Information

    hep-th 2025-06 unverdicted novelty 3.0 of 10

    Takayanagi's essay outlines a research program in which holographic spacetime, including the time direction, may emerge from entanglement, complexity, and complex-valued pseudo-entropy, without presenting a new derivation.

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