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

A bstract We study the (type 0B) $$ \mathcal{N} $$ N = 1 supersymmetric complex Liouville string (S ℂ LS), a supersymmetric extension of the bosonic complex Liouville string ( ℂ 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 ℂ 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 S ℂ LS is the same as that for the bosonic ℂ LS. We also investigate a related theory $$ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $$ S ℂ LS ̂ , which differs in the gauged worldsheet supersymmetry. A parallel analysis is performed for $$ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $$ S ℂ 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 S ℂ LS and $$ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $$ S ℂ LS ̂ .