Rectangular W-(super)algebras and their representations

Abstract

We study W-algebras obtained by quantum Hamiltonian reduction of $sl(Mn)$ associated to the $sl(2)$ embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with $M\times M$ matrix valued fields. In our previous work, we examined the basic properties of the W-algebra and claimed that the algebra can be realized as the symmetry of Grassmannian-like coset even with finite central charge based on a proposal of holography. In this paper, we extend the analysis in the following ways. First, we compute the operator product expansions among low spin generators removing the restriction of $n=2$. Second, we investigate the degenerate representations in several ways, and see the relations to the coset spectrum and the conical defect geometry of the higher spin gravity. For these analyses, we mainly set $M=n=2$. Finally, we extend the previous analysis by introducing $\mathcal{N}=2$ supersymmetry.

49 pages, minor changes, published version

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Cited by in corpus (16)

• 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
• 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 $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• More on Affine Dynkin Quiver Yangians
• Adding Complex Fermions to the Grassmannian-like Coset Model
• The Grassmannian VOA
• Invariant subalgebras of the small $\mathcal{N}=4$ superconformal algebra
• The matrix-extended $W_{1+\infty }$ algebra