The rationality conjecture for the Neveu–Schwarz minimal series vertex operator superalgebras

Let $p,q\in\{2,3,4,\ldots\}$ satisfy $p-q\in 2\mathbb Z$, with $(p-q)/2$ and $q$ relatively prime, and set

$$c_{p,q}=\frac{3}{2}\left(1-\frac{2(p-q)^2}{pq}\right),$$ $$h_{p,q}^{r,s}=\frac{(sp-rq)^2-(p-q)^2}{8pq}.$$

Write $V_{c_{p,q}}$ for the vertex operator superalgebra at central charge $c_{p,q}$, and let $L_{c,h_{r,s}}$ denote the minimal series module of central charge $c=c_{p,q}$ and highest weight $h_{r,s}=h_{p,q}^{r,s}$.

Rationality conjecture. The vertex operator superalgebra $V_{c_{p,q}}$ is rational. Moreover, the minimal series modules $L_{c,h_{r,s}}$, with $0<r<p$, $0<s<q$, and $r-s\in 2\mathbb Z$, are all the irreducible representations of $V_c$.

This is the proposed analogue for vertex operator superalgebras of the rationality and classification result for the Virasoro minimal series. The supplied text gives no resolution, so the conjecture is recorded as open.