Duality in N=2 minimal model holography

Abstract

Recently a duality between a family of \mathcal{N}=2 supersymmetric higher spin theories on AdS3, and the 't Hooft like limit of a class of Kazama-Suzuki models (that are parametrised by N and k) was proposed. The higher spin theories can be described by a Chern-Simons theory based on the infinite-dimensional Lie algebra shs[μ], and under the duality, μis to be identified with λ=N/(N+k+1). Here we elucidate the structure of the (quantum) asymptotic symmetry algebra sW_{\infty}[μ] for arbitrary μand central charge c. In particular, we show that for each value of the central charge, there are generically four different values of μthat describe the same sW_{\infty} algebra. Among other things this proves that the quantum symmetries on both sides of the duality agree; this equivalence does not just hold in the 't Hooft limit, but even at finite N and k.

28 pages

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• Minimal Model Holography
• Black holes in three dimensional higher spin gravity: A review
• Large N=4 Holography
• String Theory as a Higher Spin Theory
• Webs of W-algebras
• Extended higher spin holography and Grassmannian models
• N=1 supersymmetric higher spin holography on AdS_3
• W Symmetry and Integrability of Higher spin black holes
• N=1 extension of minimal model holography
• Three point functions in higher spin AdS_3 supergravity
• Instanton R-matrix and W-symmetry
• On the coset duals of extended higher spin theories
• The supersymmetric affine Yangian
• Three-Point Functions in N=2 Higher-Spin Holography
• Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• Conical defects and N=2 higher spin holography
• Rectangular W-algebras, extended higher spin gravity and dual coset CFTs
• Higher Spin Currents in the N=1 Stringy Coset Minimal Model
• Higher spin algebras and large $\mathcal{N}=4$ holography
• Rectangular W-(super)algebras and their representations
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• Higher Spin Currents with Arbitrary N in the N=1 Stringy Coset Minimal Model
• Dualities from higher-spin supergravity
• The Continuous Orbifold of N=2 Minimal Model Holography
• The Stranger Things of Symmetric Product Orbifold CFTs
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• Galilean contractions of $W$-algebras
• The geometry of the limit of N=2 minimal models
• The large $\mathcal{N}=4$ superconformal ${\mathcal{W}}_{\infty }$ algebra
• Chiral Algebras of Two-Dimensional SYK Models
• Gluing two affine Yangians of ${\mathfrak{gl}}_1$
• Higher Spin Currents in Wolf Space for Generic N
• Extremal Higher Spin Black Holes
• Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs
• The symmetric orbifold of N=2 minimal models
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• ABJ Theory in the Higher Spin Limit
• Holographic Renormalisation for the Spin-3 Theory and the (A)dS3/CFT2 correspondence
• Limit theories and continuous orbifolds
• Adding Complex Fermions to the Grassmannian-like Coset Model
• A note on the $\mathcal{N}=2$ super-${\mathcal{W}}_3$ holographic dictionary
• Toward a Higher-Spin Dual of Interacting Field Theories
• The Grassmannian-like Coset Model and the Higher Spin Currents
• Higher Spin Gravity and Exact Holography
• The large level limit of Kazama-Suzuki models
• The matrix-extended $W_{1+\infty }$ algebra
• The Small $\mathcal{N}=4$ Superconformal ${\mathcal{W}}_{\infty }$ Algebra
• Self-Duality from New Massive Gravity Holography