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

Abstract

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 $$ \mathcal{N} $$ N = 1 supersymmetry.