Generalized Supergravity Equations for the WZW Model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909409827880960 |
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| author | Eghbali, Ali Ghasemi-Sorkhabi, Simin Rezaei-Aghdam, Adel |
| author_facet | Eghbali, Ali Ghasemi-Sorkhabi, Simin Rezaei-Aghdam, Adel |
| contents | Generalized supergravity equations (GSEs) were originally proposed as a modification of the standard IIB supergravity equations to satisfy the background of $η$-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 ${\cal L}_{_{I}} G_{_{μν}}=0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Supergravity Equations for the WZW Model Eghbali, Ali Ghasemi-Sorkhabi, Simin Rezaei-Aghdam, Adel High Energy Physics - Theory Generalized supergravity equations (GSEs) were originally proposed as a modification of the standard IIB supergravity equations to satisfy the background of $η$-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 ${\cal L}_{_{I}} G_{_{μν}}=0$ 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. |
| title | Generalized Supergravity Equations for the WZW Model |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.17399 |