C2-cofiniteness characterization of Neveu–Schwarz minimal series representations

Let $M$ be a simple module over the Neveu–Schwarz Lie superalgebra $\mathfrak{g}$ with central charge $c$. The module $M$ is considered as a module over the Neveu–Schwarz SUSY vertex algebra $V^c$.

Neveu–Schwarz minimal-series conjecture. The following conditions are equivalent:

• $M$ is $C_2$-cofinite as a module over the Neveu–Schwarz SUSY vertex algebra $V^c$.
• $M$ is a minimal series representation of $\mathfrak{g}$.

The analogous equivalence is known for highest-weight modules over the Virasoro algebra, while the author states that it is not known whether the same argument applies to Neveu–Schwarz minimal representations. This conjecture proposes the corresponding characterization in the Neveu–Schwarz setting.