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Abstract
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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.
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