Towards the super Virasoro minimal string

TL;DR

This paper extends the bosonic Virasoro minimal string to an $ =1$ supersymmetric version, exploring its worldsheet theory with super Liouville components and proposing a dual matrix model, with initial verification of some amplitude predictions.

Contribution

It defines the timelike super Liouville theory spectrum and structure constants, and predicts vanishing amplitudes in the dual supergravity matrix model, advancing the understanding of superstring dualities.

Findings

Timelike super Liouville theory spectrum obtained

Predictions of vanishing amplitudes in 0A/0B theories confirmed for sphere three-point function

Initial verification supports the proposed duality

Abstract

The (bosonic) Virasoro minimal string, which relates worldsheet string theory to a deformation of the JT gravity matrix model, provides an interesting example of a tractable matrix/string duality. We explore its $\mathcal{N} =1$ supersymmetric generalization, the super Virasoro minimal string, which we expect to be dual to a deformation of the $\mathcal{N} =1$ JT supergravity matrix model. The worldsheet theory is characterized by two copies of super Liouville theory, one with central charge $c > \frac{27}{2}$ (the spacelike regime) and another with $c < \frac{3}{2}$ (the timelike regime), coupled to worldsheet supergravity and subject to diagonal (Type 0A/B) GSO projection. As a first step, we define the timelike theory, which has hitherto not been bootstrapped, by obtaining its spectrum and structure constants. Furthermore, we also outline the matrix model's predictions for the worldsheet observables. Curiously, all perturbative amplitudes are predicted to vanish in the 0B theory, while all tree-level amplitudes vanish in the 0A case. Using the worldsheet description, we explicitly verify this prediction (modulo an assumption) only for the simplest of the worldsheet observables, the sphere three-point function. A detailed study of other observables and verification of the duality is deferred for the future.