Generalized supergravity equations (GSEs) were originally proposed as a modification of the standard IIB supergravity equations to satisfy the background of η-deformed AdS5×S5 introduced by Arutyunov et al. In this study, we proceed to write down the GSEs for the Wess-Zumino-Witten (WZW) models based on Lie groups. First, we simplify the GSEs for the WZW model by imposing the conditions for vanishing of the one-loop beta function equations. Then, by introducing an Ansatz for the Killing vector field I, it is shown that the Killing equation LIGμν=0 is held. In addition, we introduce a generalized Killing vector such that the existence of a solution to the GSEs requires that this vector be light-like. In this way, we solve the simplified GSEs for the WZW models constructed on Lie groups up to dimension five. Unfortunately, two of the groups do not have light-like vectors and therefore do not admit the GSEs.

中文翻译：

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WZW 模型的广义超重力方程


广义超重力方程 （GSE） 最初是作为标准 IIB 超重力方程的修改而提出的，以满足 Arutyunov 等人提出的η变形 AdS5×S5 的背景。在这项研究中，我们继续写下基于 Lie 组的 Wess-Zumino-Witten （WZW） 模型的 GSE。首先，我们通过施加单环 beta 函数方程消失的条件来简化 WZW 模型的 GSE。然后，通过为 Killing 向量场 I 引入 Ansatz，表明 Killing 方程 LIGμν=0 成立。此外，我们引入了一个广义的 Killing 向量，使得 GSE 解的存在要求该向量是类似光的。通过这种方式，我们求解了在李群（最大维度 5）上构建的 WZW 模型的简化 GSE。不幸的是，其中两个组没有类似光的向量，因此不允许 GSE。