INVARIANT SUBALGEBRAS OF THE SMALL 𝒩 = 4 SUPERCONFORMAL ALGEBRA

Abstract

Various aspects of orbifolds and cosets of the small 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 𝒩 = 4 superconformal algebra with Com(Vℓ(𝔰𝔩2); Vℓ+1(𝔰𝔩2) ⊗ 𝒲–5/2(𝔰𝔩4; frect)) and in addition at special levels with Grassmanian cosets and principal 𝒲-algebras of type A at degenerate admissible levels. These coincidences lead us to a novel level-rank duality involving Grassmannian supercosets.