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The semiclassical limit of W N CFTs and Vasiliev theory

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Abstract

We propose a refinement of the Gaberdiel-Gopakumar duality conjecture between W N conformal field theories and 2+1-dimensional higher spin gravity. We make an identification of generic representations of the W N CFT in the semiclassical limit with bulk configurations. By studying the spectrum of the semiclassical limit of the W N theories and mapping to solutions of Euclidean Vasiliev gravity at λ = −N, we propose that the ‘light states’ of the W N minimal models in the ’t Hooft limit map not to the conical defects of the Vasiliev theory, but rather to bound states of perturbative scalar fields with these defects. Evidence for this identification comes from comparing charges and from holographic relations between CFT null states and bulk symmetries. We also make progress in understanding the coupling of scalar matter to sl(N) gauge fields.

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Authors and Affiliations

  1. DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0WA, U.K.

    Eric Perlmutter

  2. Institute of Physics of the ASCR, Na Slovance 2, 182 21, Prague 8, Czech Republic

    Tomáš Procházka & Joris Raeymaekers

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  1. Eric Perlmutter
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  2. Tomáš Procházka
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  3. Joris Raeymaekers
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Correspondence to Tomáš Procházka.

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ArXiv ePrint: 1210.8452

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Perlmutter, E., Procházka, T. & Raeymaekers, J. The semiclassical limit of W N CFTs and Vasiliev theory. J. High Energ. Phys. 2013, 7 (2013). https://doi.org/10.1007/JHEP05(2013)007

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  • DOI: https://doi.org/10.1007/JHEP05(2013)007

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