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Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 07 July 2021

Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

  • Suting Zhao  ORCID: orcid.org/0000-0001-7877-01421,
  • Christian Northe1 &
  • René Meyer1 

Journal of High Energy Physics volume 2021, Article number: 30 (2021) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of \( \hat{\mathfrak{u}}{(1)}_k \) Kac-Moody type. Employing the \( \hat{\mathfrak{u}}{(1)}_k \) Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

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Authors and Affiliations

  1. Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    Suting Zhao, Christian Northe & René Meyer

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  1. Suting Zhao
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  2. Christian Northe
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Zhao, S., Northe, C. & Meyer, R. Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory. J. High Energ. Phys. 2021, 30 (2021). https://doi.org/10.1007/JHEP07(2021)030

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  • Received: 21 January 2021

  • Revised: 31 March 2021

  • Accepted: 14 June 2021

  • Published: 07 July 2021

  • DOI: https://doi.org/10.1007/JHEP07(2021)030

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Keywords

  • AdS-CFT Correspondence
  • Gauge-gravity correspondence
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