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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.07972 |
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| _version_ | 1866914794349527040 |
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| author | de Gioia, Leonardo Pipolo Raclariu, Ana-Maria |
| author_facet | de Gioia, Leonardo Pipolo Raclariu, Ana-Maria |
| contents | We show that two- and three-point celestial (C)CFT$_{d-1}$ amplitudes can be directly obtained from correlation functions in a unitary Lorentzian CFT$_d$ on $\mathbb{R}\times S^{d-1}$. The recipe involves a rescaling of the operators, followed by an expansion around a bulk point configuration and a transformation to an $S^{d-1}$ conformal primary basis. The first two steps project the CFT$_d$ correlators onto distributions on $S^{d-1}$. The final step implements a dimensional reduction yielding CCFT$_{d-1}$ amplitudes that are manifestly vanishing for all in/out configurations and Poincaré invariant. The dimensional reduction may be implemented either by evaluating certain time integral transforms around the bulk-point limit, or by analytically continuing the CFT$_d$ operator dimensions and restricting the operators to $S^{d-1}$ time slices separated by $π$ in global time. The latter prescription generates the correct normalization for both two- and three-point functions. On the other hand, the celestial three-point amplitudes obtained via the former prescription are found to only agree after evaluating a residue at an integer linear combination of the CFT$_d$ conformal dimensions. The correct normalization may also be obtained by considering a different integration path in the uplift of the complexified time plane to its universal cover. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Celestial amplitudes from conformal correlators with bulk-point kinematics de Gioia, Leonardo Pipolo Raclariu, Ana-Maria High Energy Physics - Theory We show that two- and three-point celestial (C)CFT$_{d-1}$ amplitudes can be directly obtained from correlation functions in a unitary Lorentzian CFT$_d$ on $\mathbb{R}\times S^{d-1}$. The recipe involves a rescaling of the operators, followed by an expansion around a bulk point configuration and a transformation to an $S^{d-1}$ conformal primary basis. The first two steps project the CFT$_d$ correlators onto distributions on $S^{d-1}$. The final step implements a dimensional reduction yielding CCFT$_{d-1}$ amplitudes that are manifestly vanishing for all in/out configurations and Poincaré invariant. The dimensional reduction may be implemented either by evaluating certain time integral transforms around the bulk-point limit, or by analytically continuing the CFT$_d$ operator dimensions and restricting the operators to $S^{d-1}$ time slices separated by $π$ in global time. The latter prescription generates the correct normalization for both two- and three-point functions. On the other hand, the celestial three-point amplitudes obtained via the former prescription are found to only agree after evaluating a residue at an integer linear combination of the CFT$_d$ conformal dimensions. The correct normalization may also be obtained by considering a different integration path in the uplift of the complexified time plane to its universal cover. |
| title | Celestial amplitudes from conformal correlators with bulk-point kinematics |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.07972 |