Limits of minimal models and continuous orbifolds

Abstract

The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be equivalent to the singlet sector of a free boson theory, thus paralleling exactly the structure of the free theory in the Klebanov-Polyakov proposal. In 2d, the singlet sector does not describe a consistent theory by itself since the corresponding partition function is not modular invariant. However, it can be interpreted as the untwisted sector of a continuous orbifold, and this point of view suggests that it can be made consistent by adding in the appropriate twisted sectors. We show that these twisted sectors account for the `light states' that were not included in the original 't Hooft limit. We also show that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold agrees precisely with the limit theory of Runkel & Watts. In particular, this implies that our construction satisfies crossing symmetry.

33 pages; v2: minor improvements and references added, published version

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Cited by in corpus (26)

• Triality in Minimal Model Holography
• Higher Spins & Strings
• Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity
• Higher spin gravity in 3D: black holes, global charges and thermodynamics
• Higher spin black hole entropy in three dimensions
• Duality in N=2 minimal model holography
• String Universality for Permutation Orbifolds
• Extended higher spin holography and Grassmannian models
• Supersymmetric holography on AdS3
• W Symmetry and Integrability of Higher spin black holes
• Light States in Chern-Simons Theory Coupled to Fundamental Matter
• Perturbations of W(infinity) CFTs
• The Large N 't Hooft Limit of Kazama-Suzuki Model
• Three-Point Functions in N=2 Higher-Spin Holography
• The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models
• Higher Spin Currents in the N=1 Stringy Coset Minimal Model
• Higher spins in the symmetric orbifold of K3
• Higher spin algebras and large $\mathcal{N}=4$ holography
• The Continuous Orbifold of N=2 Minimal Model Holography
• Reflection and transmission of conformal perturbation defects
• The Spectrum of Light States in Large N Minimal Models
• Double Trace Interfaces
• Twisted sectors from plane partitions
• The limit of N=(2,2) superconformal minimal models
• Even spin $\mathcal{N}=4$ holography
• Non-Abelian T-duality and Modular Invariance