Exact conformal field theories from mutually T-dualizable σ-models

Exact conformal field theories (CFI's) are obtained by using the approach of Poisson-Lie (PL) T-duality in the presence of spectators. We explicitly construct some non-Abelian T-dual sigma-models (here as the PL T-duality on a semi-Abelian double) on 2+ 2-dimensional target manifolds M approximate to O x G and (M) over tilde approximate to O x (G) over tilde, where G and (G) over tilde as two-dimensional real non-Abelian and Abelian Lie groups act freely on M and Sf, respectively, while O is the orbit of G in M. The findings of our study show that the original models are equivalent to Wess-Zumino-Witten (WZW) models based on the Heisenberg (H-4) and GL(2, R) Lie groups. In this way, some new T-dual backgrounds for these WZW models are obtained. For one of the duals of the H-4 WZW model, we show that the model is self-dual. In the case of the GL(2, R) WZW model it is observed that the duality transformation changes the asymptotic behavior of solutions from AdS(3) x R to flat space. Then, the structure and asymptotic nature of the dual spacetime of this model including the horizon and singularity are determined. We furthermore get the noncritical Bianchi type III string cosmological model with a nonvanishing field strength from T-dualizable sigma-models and show that this model describes an exact CFT (equivalent to the GL(2, R) WZW model). After that, the conformal invariance of T-dual models up to two-loop order (first order in alpha') is discussed.