论文标题
基于非符号简单组和平面波目标空间的可集成模型
Integrable models based on non-semi-simple groups and plane wave target spacetimes
论文作者
论文摘要
我们启动基于非偏simimple群体的可集成$λ$成型的WZW型号的构建。我们专注于四维案例，其基础对称性基于非偏见组$ e_2^c $。 Lorentzian签名的相应重力背景是平面波，可以作为$λ$ -Defformed $ su（2）$背景乘以$λ$ -MATRIX的适当选择的$λ$ -Defformed $ su（2）$背景的penrose限制。我们构建了两个这样的变形，我们证明是可以集成的。它们都变形了纳皮的平面波，并且是不相等的。然而，它们具有相同的基础对称代数，这是$λ$ - 定型的$ su（2）$背景的saletan型收缩。我们还从$ \ nicefrac {su（2）} {u（1）} $ coset cft的$λ$形式的penrose限制构建了一个平面波，该平台timpers times times timelike坐标代表了过去构建的对数CFT的变形。最后，我们基于最简单的杨巴克斯特$σ$ - 模型简要考虑收缩。
We initiate the construction of integrable $λ$-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 $λ$-deformed $SU(2)$ background times a timelike coordinate for appropriate choices of the $λ$-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 $λ$-deformed $SU(2)$ background with a timelike direction. We also construct a plane wave from the Penrose limit of the $λ$-deformation of the $\nicefrac{SU(2)}{U(1)}$ 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 $σ$-models.
