T-dualization of G\xf6del string cosmologies via Poisson\u2013Lie 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 ' 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 '-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 AdS_3 times mathbb {R} space is discussed.