Integrable models based on non-semi-simple groups and plane wave target spacetimes

We initiate the construction of integrable lambda-deformed WZW models based on non-semisimple groups. We focus on the four-dimensional case whose underlying symmetries are based on the non-semisimple group E-2(c). The corresponding gravitational backgrounds of Lorentzian signature are plane waves which can be obtained as Penrose limits of the lambda-deformed SU(2) background times a timelike coordinate for appropriate choices of the lambda-matrix. We construct two such deformations which we demonstrate to be integrable. They both deform the Nappi-Witten plane wave and are inequivalent. Nevertheless, they have the same underlying symmetry algebra which is a Saletan-type contraction of that for the lambda-deformed SU(2) background with a timelike direction. We also construct a plane wave from the Penrose limit of the lambda-deformation of the SU(2)/U(1) coset CFT times a timelike coordinate which represents the deformation of a logarithmic CFT constructed in the past. Finally, we briefly consider contractions based on the simplest Yang-baxter sigma-models.

Automated summary

This article focuses on the construction of integrable lambda-deformed WZW models based on non-semisimple groups. Two different deformations of the Nappi-Witten plane wave with the same underlying symmetry algebra are constructed for the four-dimensional case. Additionally, a plane wave representing the deformation of a logarithmic CFT is constructed from the Penrose limit of the lambda deformation of the SU(2)/U(1) coset CFT.