$\mathcal{N}=1$ super complex Liouville string

TL;DR

This paper extends the bosonic complex Liouville string to an $ ext{N}=1$ supersymmetric version, computes key amplitudes, and proposes dual matrix models, finding strong parallels with the bosonic case through analytical and numerical evidence.

Contribution

It introduces the supersymmetric complex Liouville string, computes its amplitudes, and suggests that its dual matrix model is identical to the bosonic case, supported by analytical and numerical analysis.

Findings

Sphere three-point amplitudes match the bosonic case.

Four-point amplitude structure is identical to the bosonic case.

Numerical evaluation supports the proposed dual matrix models.

Abstract

We study the (type 0B) $\mathcal{N}=1$ supersymmetric complex Liouville string ($\text{S}\mathbb{C}\text{LS}$), a supersymmetric extension of the bosonic complex Liouville string ($\mathbb{C}\text{LS}$). We compute the sphere three-point amplitudes (including NS-NS-NS and NS-R-R types) and find they share the same form as the sphere three-point amplitude of the bosonic $\mathbb{C}\text{LS}$. Analysis of the analytic structure of the NS-NS-NS-NS four-point amplitude and the higher equations of motion also yields results identical to the bosonic case. Based on these findings, we propose that the dual matrix model for the $\text{S}\mathbb{C}\text{LS}$ is the same as that for the bosonic $\mathbb{C}\text{LS}$. We also investigate a related theory $\widehat{\text{S}\mathbb{C}\text{LS}}$, which differs in the gauged worldsheet supersymmetry. A parallel analysis is performed for $\widehat{\text{S}\mathbb{C}\text{LS}}$, and a candidate for its dual matrix model is proposed. We then carry out a partial numerical evaluation of the moduli space integral, which provides further evidence for both the proposals of the dual matrix model regarding $\text{S}\mathbb{C}\text{LS}$ and $\widehat{\text{S}\mathbb{C}\text{LS}}$.