Invariant subalgebras of the small $\mathcal{N}=4$ superconformal algebra

Abstract

Various aspects of orbifolds and cosets of the small $\mathcal{N}=4$ superconformal algebra are studied. First, we determine minimal strong generators for generic and specific levels. As a corollary, we obtain the vertex algebra of global sections of the chiral de Rham complex on any complex Enriques surface. We also identify orbifolds of cosets of the small $\mathcal{N}=4$ superconformal algebra with $\text{Com}(V^{\ell }({\mathfrak{sl}}_2),V^{\ell +1}({\mathfrak{sl}}_2)\otimes {\mathcal{W}}_{-5/2}({\mathfrak{sl}}_4,f_{\text{rect}}))$ and in addition at special levels with Grassmanian cosets and principal $\mathcal{W}$-algebras of type $A$ at degenerate admissible levels. These coincidences lead us to a novel level-rank duality involving Grassmannian supercosets.

Many corrections and improvements to the exposition. Conjecture 7.9 from previous version is now a theorem

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Cited by in corpus (2)

• $N=4$ superconformal algebras and diagonal cosets
• Cosets of free field algebras via arc spaces