T-dualization of Gödel string cosmologies via Poisson-Lie T-duality approach

Abstract

Using the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in ${\alpha }^{\prime }$ including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson-Lie (PL) T-duality approach. In studying Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to ${\alpha }^{\prime }$-corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as $A_2$, $A_2\oplus A_1$ and $SL(2,\mathbb{R})$. In this way, the PL self-duality of $Ad{S}_3\times \mathbb{R}$ space is discussed.

44 pages; two references and three Tables added

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Cited by in corpus (4)

• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Non-Abelian T-duality of $Ad{S}_{d\le 3}$ families by Poisson-Lie T-duality
• Non-Abelian target space duals of Thurston geometries
• Regular $(2+1)$-dimensional spatially homogeneous ${\alpha }^{\prime }$-corrected BTZ-like black hole in string theory