Even spin minimal model holography

Abstract

The even spin W^e_\infty algebra that is generated by the stress energy tensor together with one Virasoro primary field for every even spin s \geq 4 is analysed systematically by studying the constraints coming from the Jacobi identities. It is found that the algebra is characterised, in addition to the central charge, by one free parameter that can be identified with the self-coupling constant of the spin 4 field. We show that W^e_\infty can be thought of as the quantisation of the asymptotic symmetry algebra of the even higher spin theory on AdS_3. On the other hand, W^e_\infty is also quantum equivalent to the so(N) coset algebras, and thus our result establishes an important aspect of the even spin minimal model holography conjecture. The quantum equivalence holds actually at finite central charge, and hence opens the way towards understanding the duality beyond the leading 't Hooft limit.

32 pages, v2: reference added, minor changes in text

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• Instanton R-matrix and W-symmetry
• On the coset duals of extended higher spin theories
• Conical defects and N=2 higher spin holography
• Conical Defects, Black Holes and Higher Spin (Super-)Symmetry
• 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
• Sub-AdS Scale Locality in AdS${}_3$/CFT${}_2$
• Higher Spin Currents in the Holographic N=1 Coset Minimal Model
• Higher Spin Currents in Wolf Space for Generic N
• Higher Spin Currents in Orthogonal Wolf Space
• Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs
• $N=4$ superconformal algebras and diagonal cosets
• The Next $16$ Higher Spin Currents and Three-Point Functions in the Large $\mathcal{N}=4$ Holography
• Even spin $\mathcal{N}=4$ holography
• Toda theory in AdS${}_2$ and $\mathcal{W}{A}_n$-algebra structure of boundary correlators
• Higher Spin Currents in the Orthogonal Coset Theory
• Conformal embeddings and higher-spin bulk duals
• Symmetry Algebras of Stringy Cosets
• On even spin $W_{\infty }$
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• The Higher Spin Rectangle
• The Grassmannian VOA
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories