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arXiv · 1906.05872

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

Thomas Creutzig·Yasuaki Hikida·Takahiro Uetoko
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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.

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Thomas Creutzig, Yasuaki Hikida, Takahiro Uetoko. 2019-09-24. Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs. https://doi.org/10.1007/jhep10(2019)023

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