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

摘要

Exact conformal field theories (CFTs) 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 σ-models (here as the PLTduality on a semi-Abelian double) on 2 + 2-dimensional target manifolds M ≈ O × G and M ≈ O × G, where G and G as two-dimensional real non-Abelian and Abelian Lie groups act freely on M and M , 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 H4 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 AdS3 × 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 σ-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 α0) is discussed.