Abstract
We generalize the formulation of Poisson-Lie (PL) T-plurality proposed by R. von Unge (2002) [6] from Lie groups to Lie supergroups. By taking a convenient ansatz for metric of the σ-model in terms of the left-invariant one-forms of the isometry Lie supergroups (C3+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 (C3+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.
Highlights
In this paper we firstly recall the definitions of Manin supertriple and Drinfeld superdoubles (DSDs) and briefly explain the construction of PL T-dual σ-models on Lie supergroups
It is shown that the resulting backgrounds are equivalent to the ones of T-dual σ-models constructing on semi-Abelian DSDs ((C 3 + A ), I(2|2) ) and (gl(1|1), I(2|2) ) where I(2|2) is four-dimensional Abelian Lie supergroup of the type (2|2)
Using the formulation of super PL T-plurality and starting from the aforementioned decompositions of DSDs we find the conformal duality chains of 2+1-dimensional cosmological string backgrounds coupling with two fermionic fields
Summary
As in conventional general relativity, homogeneous backgrounds in string cosmology may be defined as those 3 + 1-dimensional spacetime manifolds which admit a 3-parameter group of isometries. It has been shown that [26–29] Bianchi-type string cosmology involves 3 + 1dimensional spatially homogeneous spacetimes which satisfy at least the lowest-order string beta-function equations. Bianchi-type cosmologies can be generally defined in terms of a three-dimensional real Lie group of isometries that act -transitively on three-dimensional, space like orbits [26,29] (see [30,31] and references therein). These models were generalized to 4 + 1-dimensional cosmological models with four-dimensional real Lie groups whose spatial hypersurfaces are () connected homogeneous Riemannian manifolds [32] (see [33]). We present some new solutions of string cosmological models on supermanifolds characterized by (2 + 1|2)-dimensional metric (with four-dimensional Lie supergroups of the type (2|2) as isometry supergroups), a dilaton field at most a function of t only and vanishing torsion
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