Orthosymplectic W-algebra rationality conjecture

Let $m\geq 1$ and set

$$\psi=\frac{p}{2(p+q)}.$$

Assume that $p,q\in\mathbb{N}$ are coprime, that $p\geq 2m-1$ when $q$ is odd, and that $p\geq 2m$ when $q$ is even. Orthosymplectic W-algebra rationality conjecture. The vertex superalgebra $\mathcal W_{\psi-m-1/2}(\mathfrak{osp}_{1|2m})$ is lisse and rational. Consequently, at the Feigin–Frenkel dual level $\psi'=1/(4\psi)=(p+q)/(2p)$, the corresponding algebra is also expected to be lisse and rational. This is the orthosymplectic analogue of Arakawa's rationality theorem for W-algebras of simple Lie algebras; the conjecture is motivated by a coset realization.