论文标题
基于Lie SuperGroups的WZW模型的Yang-Baxter变形：$ GL（1 | 1）$和$（C^3 +A）$的情况
Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3 +A)$
论文作者
论文摘要
我们继续将Wess-Zumino-Witten（WZW）模型的Yang-Baxter（YB）变形概括为Lie SuperGroups案例。这种概括使我们能够利用（修改的）经典Yang-baxter方程（（（M）GCYBE）的各种解决方案，根据Lie SuperGroups对WZW模型的YB变形进行分类。我们为$ gl（1 | 1）$和$（{\ cal c}^3 +{\ cal a}）$在非标准的基础上获得了$ gl（1 | 1）$和$（{\ cal c}^3 +{\ cal a}）$的（M）gcybe的不相等的解决方案（经典的R-Matrices），以相应的自动化转换为基础。然后，基于$ gl（1 | 1）$和$（c^3 + a）$ lie SuperGroups的WZW模型的YB变形由满足（M）GCYBE的偏斜式经典R-Matrices指定。在某些情况下，对于两种变形模型的家族，指标在变形下仍然不变，而$ b $ fields的组件被更改。在检查模型的保形不变性之后，得出的结论是，$ gl（1 | 1）$和$（c^3 + a）$ WZW型号是保留YB变形的类别中保留构造中不变性的同类理论。但是，我们的结果本身很有趣，但是在建设性的水平上，可能会促使许多新的见解（广义）超级实力解决方案。
We proceed to generalize the Yang-Baxter (YB) deformation of Wess-Zumino-Witten (WZW) model to the Lie supergroups case. This generalization enables us to utilize various kinds of solutions of the (modified) graded classical Yang-Baxter equation ((m)GCYBE) to classify the YB deformations of WZW models based on the Lie supergroups. We obtain the inequivalent solutions (classical r-matrices) of the (m)GCYBE for the $gl(1|1)$ and $({\cal C}^3 +{\cal A})$ Lie superalgebras in the non-standard basis, in such a way that the corresponding automorphism transformations are employed. Then, the YB deformations of the WZW models based on the $GL(1|1)$ and $(C^3 + A)$ Lie supergroups are specified by skew-supersymmetric classical r-matrices satisfying (m)GCYBE. In some cases for both families of deformed models, the metrics remain invariant under the deformation, while the components of $B$-fields are changed. After checking the conformal invariance of the models up to one-loop order, it is concluded that the $GL(1|1)$ and $(C^3 + A)$ WZW models are conformal theories within the classes of the YB deformations preserving the conformal invariance. However, our results are interesting in themselves, but at a constructive level, may prompt many new insights into (generalized) supergravity solutions.
