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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2404.09655 |
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| _version_ | 1866929314118762496 |
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| author | Imaanpur, Ali |
| author_facet | Imaanpur, Ali |
| contents | The metric of $S^7$ can be written as an $SU(2)$-instanton bundle over $S^4$. It is also possible to write it differently as an anti-instanton bundle. We use this observation to construct an instanton--anti-instanton, $SU(2)\times SU(2)$, bundle over $S^4$. We show that this 10d manifold admits two Einstein metrics. We then rewrite the metric to isolate two $U(1)$ directions of the fibre and dimensionally reduce along them to get an eight dimensional metric describing an $S^2\times S^2$ bundle over $S^4$. This metric allows a harmonic 4-form which we use to derive new supergravity solutions in eleven and ten dimensions as $AdS_3\times M_8$ and $AdS_2\times M_8$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09655 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An $S^3\times S^3$ bundle over $S^4$ and new supergravity solutions Imaanpur, Ali High Energy Physics - Theory Mathematical Physics The metric of $S^7$ can be written as an $SU(2)$-instanton bundle over $S^4$. It is also possible to write it differently as an anti-instanton bundle. We use this observation to construct an instanton--anti-instanton, $SU(2)\times SU(2)$, bundle over $S^4$. We show that this 10d manifold admits two Einstein metrics. We then rewrite the metric to isolate two $U(1)$ directions of the fibre and dimensionally reduce along them to get an eight dimensional metric describing an $S^2\times S^2$ bundle over $S^4$. This metric allows a harmonic 4-form which we use to derive new supergravity solutions in eleven and ten dimensions as $AdS_3\times M_8$ and $AdS_2\times M_8$, respectively. |
| title | An $S^3\times S^3$ bundle over $S^4$ and new supergravity solutions |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2404.09655 |