The Large N 't Hooft Limit of Coset Minimal Models

Abstract

Recently, Gaberdiel and Gopakumar proposed that the two-dimensional WA_{N-1} minimal model conformal field theory in the large N 't Hooft limit is dual to the higher spin theories on the three-dimensional AdS space with two complex scalars. In this paper, we examine this proposal for the WD_{N/2} and WB_{(N-1)/2} minimal models initiated by Fateev and Lukyanov in 1988. By analyzing the renormalization group flows on these models, we find that the gravity duals in AdS space are higher spin theories coupled to two equally massive real scalar fields. We also describe the large N 't Hooft limit for the minimal model of the second parafermion theory.

24 pages; footnotes 4 and 6 added, the pages 11-12 improved and to appear in JHEP

References in corpus (6)

• Symmetries of Holographic Minimal Models
• Partition Functions of Holographic Minimal Models
• Quantum W-symmetry in AdS_3
• Renormalization group flows for $Z_5$ parafermionic field theory
• Renormalization group flows for the second $Z_N$ parafermionic field theory for N odd
• Renormalization group flows for the second ${\mathbb{Z}}_N$ parafermionic field theory for $N$ even

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