Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs

Abstract

We examine rectangular W-algebras with $so(M)$ or $sp(2M)$ symmetry, which can be realized as the asymptotic symmetry of higher spin gravities with restricted matrix extensions. We compute the central charges of the algebras and the levels of $so(M)$ or $sp(2M)$ affine subalgebras by applying the Hamiltonian reductions of $so$ or $sp$ type Lie algebras. For simple cases with generators of spin up to two, we obtain their operator product expansions by requiring the associativity. We further claim that the W-algebras can be realized as the symmetry algebras of dual coset CFTs and provide several strong supports. The analysis can be regarded as a check of extended higher spin holographies including full quantum corrections. We also extend the analysis by introducing $\mathcal{N}=1$ supersymmetry.

arXiv comment49 pages, 2 tables, alternative proposals of dual coset models added, a reference added, published version

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Cited by in corpus (8)

• Rectangular W-(super)algebras and their representations
• Toward A Supersymmetric $w_{1+\infty }$ Symmetry in the Celestial Conformal Field Theory
• Correspondences among CFTs with different W-algebra symmetry
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• More on Affine Dynkin Quiver Yangians
• Adding Complex Fermions to the Grassmannian-like Coset Model
• The Grassmannian-like Coset Model and the Higher Spin Currents
• The matrix-extended $W_{1+\infty }$ algebra