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| Natura: | Preprint |
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2021
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| Accesso online: | https://arxiv.org/abs/2110.06180 |
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| _version_ | 1866909552448897024 |
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| author | Bhattacharjee, Budhaditya Krishnan, Chethan |
| author_facet | Bhattacharjee, Budhaditya Krishnan, Chethan |
| contents | We consider the analytic continuation of $(p+q)$-dimensional Minkowski space (with $p$ and $q$ even) to $(p,q)$-signature, and study the conformal boundary of the resulting "Klein space". Unlike the familiar $(-+++..)$ signature, now the null infinity ${\mathcal I}$ has only one connected component. The spatial and timelike infinities ($i^0$ and $i'$) are quotients of generalizations of AdS spaces to non-standard signature. Together, ${\mathcal I}, i^0$ and $i'$ combine to produce the topological boundary $S^{p+q-1}$ as an $S^{p-1} \times S^{q-1}$ fibration over a null segment. The highest weight states (the $L$-primaries) and descendants of $SO(p,q)$ with integral weights give rise to natural scattering states. One can also define $H$-primaries which are highest weight with respect to a signature-mixing version of the Cartan-Weyl generators that leave a point on the celestial $S^{p-1} \times S^{q-1}$ fixed. These correspond to massless particles that emerge at that point and are Mellin transforms of plane wave states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_06180 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Celestial Klein Spaces Bhattacharjee, Budhaditya Krishnan, Chethan High Energy Physics - Theory We consider the analytic continuation of $(p+q)$-dimensional Minkowski space (with $p$ and $q$ even) to $(p,q)$-signature, and study the conformal boundary of the resulting "Klein space". Unlike the familiar $(-+++..)$ signature, now the null infinity ${\mathcal I}$ has only one connected component. The spatial and timelike infinities ($i^0$ and $i'$) are quotients of generalizations of AdS spaces to non-standard signature. Together, ${\mathcal I}, i^0$ and $i'$ combine to produce the topological boundary $S^{p+q-1}$ as an $S^{p-1} \times S^{q-1}$ fibration over a null segment. The highest weight states (the $L$-primaries) and descendants of $SO(p,q)$ with integral weights give rise to natural scattering states. One can also define $H$-primaries which are highest weight with respect to a signature-mixing version of the Cartan-Weyl generators that leave a point on the celestial $S^{p-1} \times S^{q-1}$ fixed. These correspond to massless particles that emerge at that point and are Mellin transforms of plane wave states. |
| title | Celestial Klein Spaces |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2110.06180 |