Higher spin entanglement and \( {\mathcal{W}}_{\mathrm{N}} \) conformal blocks

  • Jan de Boer
  • Alejandra Castro
  • Eliot Hijano
  • Juan I. Jottar
  • Per Kraus
Open Access
Regular Article - Theoretical Physics


Two-dimensional conformal field theories with extended \( \mathcal{W} \)-symmetry algebras have dual descriptions in terms of weakly coupled higher spin gravity in AdS3 at large central charge. Observables that can be computed and compared in the two descriptions include Rényi and entanglement entropies, and correlation functions of local operators. We develop techniques for computing these, in a manner that sheds light on when and why one can expect agreement between such quantities on each side of the duality. We set up the computation of excited state Rényi entropies in the bulk in terms of Chern-Simons connections, and show how this directly parallels the CFT computation of correlation functions. More generally, we consider the vacuum conformal block for general operators with Δ ∼ c. When two of the operators obey \( \frac{\varDelta }{c}\ll 1 \), we show by explicit computation that the vacuum conformal block is computed by a bulk Wilson line probing an asymptotically AdS3 background with higher spin fields excited, the latter emerging as the effective bulk description of the excited state produced by the heavy operators. Among other things, this puts a previous proposal for computing higher spin entanglement entropy via Wilson lines on firmer footing, and clarifies its relation to CFT. We also study the corresponding computation in Toda theory and find that this provides yet another independent way to arrive at the same result.


AdS-CFT Correspondence Conformal and W Symmetry Higher Spin Symmetry 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Jan de Boer
    • 1
  • Alejandra Castro
    • 1
  • Eliot Hijano
    • 2
  • Juan I. Jottar
    • 3
  • Per Kraus
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of Physics and AstronomyUniversity of CaliforniaLos AngelesU.S.A.
  3. 3.Institut für Theoretische PhysikETH ZürichZürichSwitzerland

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