Supermoduli-space explanation of topological recursion and vanishing amplitudes

Formulate super Virasoro minimal-string perturbation theory as an integral of an appropriate superform on supermoduli space and use that formulation to explain topological recursion for the string amplitudes and the vanishing of the stable perturbative NS amplitudes in the Type 0B$^-$ theory.

Background

The worldsheet calculations reproduce matrix-model and intersection-theory predictions only after nontrivial spin-structure sums and integrations over moduli space. In particular, the stable perturbative NS amplitudes of the Type 0B−^- theory are expected to vanish, but the cancellation is not transparent in the RNS worldsheet description.

The authors propose that a formulation directly on supermoduli space might reveal unsaturated fermionic moduli responsible for the vanishing and might clarify how the amplitudes realize topological recursion. They emphasize that even the corresponding topological-recursion structure of bosonic Virasoro minimal-string amplitudes is not currently understood.

References

Ideally, the reframing will allow one to see how the worldsheet amplitudes satisfy topological recursion and/or explain the vanishing of the #1{-} amplitudes simply from the presence of unsaturated fermionic moduli in the integrand. The former, however, seems ambitious, considering that we do not at present understand how the VMS amplitudes themselves satisfy topological recursion.

— Super Liouville theory on the torus: bootstrap and the super Virasoro minimal string  (2610.01909 - Collier et al., 1 Oct 2026) in Section 8, paragraph titled “Supermoduli space formulation of string perturbation theory”