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arXiv · 2409.17399

Generalized Supergravity Equations for the WZW Model

Ali Eghbali·Simin Ghasemi-Sorkhabi·Adel Rezaei-Aghdam
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Abstract

Generalized supergravity equations (GSEs) were originally proposed as a modification of the standard IIB supergravity equations to satisfy the background of $\eta$-deformed $AdS_5 \times S^5$ introduced by Arutyunov {\it 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 {\it Ansatz} for the Killing vector field $I$, it is shown that the Killing equation ${\cal L}_{_{I}} G_{_{\mu \nu}}=0$ 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.

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Ali Eghbali, Simin Ghasemi-Sorkhabi, Adel Rezaei-Aghdam. 2024-09-25. Generalized Supergravity Equations for the WZW Model. https://doi.org/10.1016/j.physletb.2024.139159

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