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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.15678 |
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| _version_ | 1866911558860275712 |
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| author | Heslop, P. J. Lipstein, A. E. Santagata, M. |
| author_facet | Heslop, P. J. Lipstein, A. E. Santagata, M. |
| contents | Correlators of a certain one-dimensional superconformal field theory dual to hypermultiplets in AdS$_2\times$S$^2$ exhibit a hidden four-dimensional conformal symmetry which allows one to repackage all tree-level 4-point correlators into a single four-dimensional object corresponding to a contact diagram arising from a massless $ϕ^4$ theory in AdS$_2\times$S$^2$. This theory serves as a toy model for IIB string theory in AdS$_5\times$S$^5$ and is interesting in its own right because AdS$_2\times$S$^2$ describes the near-horizon limit of extremal black holes in four dimensions. We argue that after acting with an $SU(1,1)\times SU(2)$ Casimir, all one-loop correlators can similarly be encoded by a four-dimensional function which arises from a one-loop scalar bubble diagram in AdS$_2\times$S$^2$, explaining how the hidden conformal symmetry extends beyond tree level. Finally, we conjecture a scalar effective field theory with a derivative interaction in AdS$_2\times$S$^2$ whose Witten diagrams should directly reproduce 4-point correlators to all loops without acting with Casimirs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15678 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hidden Conformal Symmetry in AdS$_2\times$S$^2$ Beyond Tree Level Heslop, P. J. Lipstein, A. E. Santagata, M. High Energy Physics - Theory Correlators of a certain one-dimensional superconformal field theory dual to hypermultiplets in AdS$_2\times$S$^2$ exhibit a hidden four-dimensional conformal symmetry which allows one to repackage all tree-level 4-point correlators into a single four-dimensional object corresponding to a contact diagram arising from a massless $ϕ^4$ theory in AdS$_2\times$S$^2$. This theory serves as a toy model for IIB string theory in AdS$_5\times$S$^5$ and is interesting in its own right because AdS$_2\times$S$^2$ describes the near-horizon limit of extremal black holes in four dimensions. We argue that after acting with an $SU(1,1)\times SU(2)$ Casimir, all one-loop correlators can similarly be encoded by a four-dimensional function which arises from a one-loop scalar bubble diagram in AdS$_2\times$S$^2$, explaining how the hidden conformal symmetry extends beyond tree level. Finally, we conjecture a scalar effective field theory with a derivative interaction in AdS$_2\times$S$^2$ whose Witten diagrams should directly reproduce 4-point correlators to all loops without acting with Casimirs. |
| title | Hidden Conformal Symmetry in AdS$_2\times$S$^2$ Beyond Tree Level |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.15678 |