Symmetries of holographic minimal models

  • Matthias R. Gaberdiel
  • Thomas HartmanEmail author


It was recently proposed that a large N limit of a family of minimal model CFTs is dual to a certain higher spin gravity theory in AdS3, where the ’t Hooft coupling constant of the CFT is related to a deformation parameter of the higher spin algebra. We identify the asymptotic symmetry algebra of the higher spin theory for generic ’t Hooft parameter, and show that it coincides with a family of \( \mathcal{W} \)-algebras previously discovered in the context of the KP hierarchy. We furthermore demonstrate that this family of \( \mathcal{W} \)-algebras controls the representation theory of the minimal model CFTs in the ’t Hooft limit. This provides a non-trivial consistency check of the proposal and explains part of the underlying mechanism.


AdS-CFT Correspondence Chern-Simons Theories Conformal and W Symmetry 


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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikETH ZurichZürichSwitzerland
  2. 2.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.

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