Cosmological string backgrounds from super Poisson-Lie T-plurality

We generalize the formulation of Poisson-Lie (PL) T-plurality proposed by R. von Unge [JHEP 07 (2002) 014] from Lie groups to Lie supergroups. By taking a convenient ansatz for metric of the $\sigma$-model in terms of the left-invariant one-forms of the isometry Lie supergroups $(C^3 +A)$ and $GL(1|1)$ we construct cosmological string backgrounds, including $(2+1|2)$-dimensional metric, time-dependent dilaton and vanishing torsion, in a way that they satisfy the one-loop beta-function equations. Starting from the decompositions of semi-Abelian Drinfeld superdoubles (DSDs) generated by the $({\C}^3 +{\A})$ and $gl(1|1)$ Lie super bi-algebras we find the conformal duality/plurality chains of $2+1$-dimensional cosmological string backgrounds coupling with two fermionic fields. In particular, the new backgrounds obtained by the super PL T-plurality remain conformally invariant at one-loop level. This work can prompt many new insights into supergravity and obviously has interesting mathematical relations with double field theory.