Rectangular W-algebras, extended higher spin gravity and dual coset CFTs

Abstract

We analyze the asymptotic symmetry of higher spin gravity with $M\times M$ matrix valued fields, which is given by rectangular W-algebras with su$(M)$ symmetry. The matrix valued extension is expected to be useful for the relation between higher spin gravity and string theory. With the truncation of spin as $s=2,3,\dots ,n$, we evaluate the central charge $c$ of the algebra and the level $k$ of the affine currents with finite $c,k$. For the simplest case with $n=2$, we obtain the operator product expansions among generators by requiring their associativity. We conjecture that the symmetry is the same as that of Grassmannian-like coset based on our proposal of higher spin holography. Comparing $c,k$ from the both theories, we obtain the map of parameters. We explicitly construct low spin generators from the coset theory, and, in particular, we reproduce the operator product expansions of the rectangular W-algebra for $n=2$. We interpret the map of parameters by decomposing the algebra in the coset description.

31 pages, minor chages, a reference added, published version

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Cited by in corpus (19)

• CFT duals of three-dimensional de Sitter gravity
• Shifted Quiver Yangians and Representations from BPS Crystals
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Gauge/Bethe correspondence from quiver BPS algebras
• Rectangular W-(super)algebras and their representations
• Toward A Supersymmetric $w_{1+\infty }$ Symmetry in the Celestial Conformal Field Theory
• $q$-Deformation of Corner Vertex Operator Algebras by Miura Transformation
• Correspondences among CFTs with different W-algebra symmetry
• Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Symmetry Algebras of Stringy Cosets
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model
• Adding Complex Fermions to the Grassmannian-like Coset Model
• The Grassmannian-like Coset Model and the Higher Spin Currents
• The Grassmannian VOA
• The matrix-extended $W_{1+\infty }$ algebra