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Charged moments in W3 higher spin holography
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  • Regular Article - Theoretical Physics
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  • Published: 25 May 2022

Charged moments in W3 higher spin holography

  • Suting Zhao  ORCID: orcid.org/0000-0001-7877-01421,
  • Christian Northe1,
  • Konstantin Weisenberger1 &
  • …
  • René Meyer1 

Journal of High Energy Physics volume 2022, Article number: 166 (2022) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

We consider the charged moments in SL(3, ℝ) higher spin holography, as well as in the dual two-dimensional conformal field theory with W3 symmetry. For the vacuum state and a single entangling interval, we show that the W3 algebra of the conformal field theory induces an entanglement W3 algebra acting on the quantum state in the entangling interval. The algebra contains a spin 3 modular charge which commutes with the modular Hamiltonian. The reduced density matrix is characterized by the modular energy and modular charge, hence our definition of the charged moments is also with respect to these conserved quantities. We evaluate the logarithm of the charged moments perturbatively in the spin 3 modular chemical potential, by computing the corresponding connected correlation functions of the modular charge operator up to quartic order in the chemical potential. This method provides access to the charged moments without using charged twist fields. Our result matches known results for the charged moment obtained from the charged topological black hole picture in SL(3, ℝ) higher spin gravity. Since our charged moments are not Gaussian in the chemical potential any longer, we conclude that the dual W3 conformal field theories must feature breakdown of equipartition of entanglement to leading order in the large c expansion.

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  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, Konstantin Weisenberger & René Meyer

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Zhao, S., Northe, C., Weisenberger, K. et al. Charged moments in W3 higher spin holography. J. High Energ. Phys. 2022, 166 (2022). https://doi.org/10.1007/JHEP05(2022)166

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  • Received: 04 March 2022

  • Revised: 02 May 2022

  • Accepted: 03 May 2022

  • Published: 25 May 2022

  • DOI: https://doi.org/10.1007/JHEP05(2022)166

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Keywords

  • AdS-CFT Correspondence
  • Gauge-Gravity Correspondence
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