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Boundary mutual information in double holography

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 13 July 2026
  • Volume 2026, article number 110 (2026)
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Journal of High Energy Physics Aims and scope Submit manuscript
Boundary mutual information in double holography
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  • Yuxuan Liu  ORCID: orcid.org/0000-0002-9852-81741,
  • Yi Ling  ORCID: orcid.org/0000-0001-7392-86412,3 &
  • Zhuo-Yu Xian  ORCID: orcid.org/0000-0002-2245-00594 

  • 148 Accesses

  • 2 Altmetric

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A preprint version of the article is available at arXiv.

Abstract

We consider a composite system where AdS3 gravity is coupled to a flat heat bath and investigate the mutual information between two subregions on the intersection of the AdS3 and bath, referred to as the boundary mutual information (BMI). The corresponding entanglement entropy is captured via quantum extremal surfaces (QES), which holographically be computed by a surface optimization algorithm based on “Surface Evolver”. We focus on both connected and disconnected configurations of the quantum entanglement wedge (Q-EW) in the AdS3 bulk and analyze the finite corrections to the BMI. Our numerical results reveal a phase transition of the BMI as the separation between two subregions increases. Furthermore, we find that the BMI can naturally be decomposed into two distinct components: a geometric term arising from the areas of the quantum extremal surfaces, and a correction term resulting from bulk quantum fields within the Q-EW. Interestingly, the geometric contribution always exceeds the total BMI, indicating a negative correction from the bulk matter fields. This negativity can be understood as the result of subtracting a greater contribution from quantum fields in the connected Q-EW than in the disconnected one. We also reproduce the negative contribution of bulk quantum fields to BMI within a random tensor network (RTN) toy model of double holography. Modeling the bulk as a highly mixed state entangled with a large bath leads to a volume-law bulk entropy. In the large bond-dimension limit, the geometric part of the BMI remains non-negative, while the bulk entropy contribution becomes non-positive when the Q-EWs merge.

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Acknowledgments

We are grateful to Alexander Jahn and Yuan Sunfor the helpful discussions. Liu Yuxuan special thanks to Peiwen Cao for supporting his work. LYX is supported by the Natural Science Foundation of China under Grant No. 12405079, the Natural Science Foundation of Hunan Province, China (Grant No. 2025JJ60062), and Research start-up funds from the Central South University. YL is supported by the Natural Science Foundation of China under Grant No. 12275275. ZYX also acknowledges support from the berlin Quantum Initiative.

Author information

Authors and Affiliations

  1. Institute of Quantum Physics, School of Physics, Central South University, Changsha, 410083, China

    Yuxuan Liu

  2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yi Ling

  3. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China

    Yi Ling

  4. Department of Physics, Freie Universität Berlin, Arnimallee 14, DE-14195, Berlin, Germany

    Zhuo-Yu Xian

Authors
  1. Yuxuan Liu
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  2. Yi Ling
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  3. Zhuo-Yu Xian
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Corresponding author

Correspondence to Yuxuan Liu.

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ArXiv ePrint: 2602.12627

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Cite this article

Liu, Y., Ling, Y. & Xian, ZY. Boundary mutual information in double holography. J. High Energ. Phys. 2026, 110 (2026). https://doi.org/10.1007/JHEP07(2026)110

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  • Received: 31 March 2026

  • Accepted: 30 May 2026

  • Published: 13 July 2026

  • Version of record: 13 July 2026

  • DOI: https://doi.org/10.1007/JHEP07(2026)110

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Keywords

  • AdS-CFT Correspondence
  • Gauge-Gravity Correspondence
  • Models of Quantum Gravity

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