Mellin amplitudes for $AdS_3 \times S^3$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929698970271744 |
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| author | Behan, Connor Pitombo, Rodrigo S. |
| author_facet | Behan, Connor Pitombo, Rodrigo S. |
| contents | There are holographic superconformal theories in all dimensions between two and six which allow arbitrary tree-level four-point functions to be fixed by basic consistency conditions. Although Mellin space is usually the most efficient setting for imposing these contraints, four-point functions in two dimensions have thus far been an exception due to their more intricate dependence on the conformal cross-ratios. In this paper, we introduce a simple fix which exploits the relation between a parity-odd conformal block in two dimensions and a parity-even conformal block in four dimensions. We then apply the resulting toolkit to a study of the paradigmatic holographic theory in two dimensions which is the D1-D5 CFT. For correlators involving Kaluza-Klein modes of the tensor multiplet, this analysis reproduces results which were previously obtained using hidden conformal symmetry. With four Kaluza-Klein modes of the graviton multiplet, it yields new results including a compact formula for the correlators of all pairwise identical operators, |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_17420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mellin amplitudes for $AdS_3 \times S^3$ Behan, Connor Pitombo, Rodrigo S. High Energy Physics - Theory There are holographic superconformal theories in all dimensions between two and six which allow arbitrary tree-level four-point functions to be fixed by basic consistency conditions. Although Mellin space is usually the most efficient setting for imposing these contraints, four-point functions in two dimensions have thus far been an exception due to their more intricate dependence on the conformal cross-ratios. In this paper, we introduce a simple fix which exploits the relation between a parity-odd conformal block in two dimensions and a parity-even conformal block in four dimensions. We then apply the resulting toolkit to a study of the paradigmatic holographic theory in two dimensions which is the D1-D5 CFT. For correlators involving Kaluza-Klein modes of the tensor multiplet, this analysis reproduces results which were previously obtained using hidden conformal symmetry. With four Kaluza-Klein modes of the graviton multiplet, it yields new results including a compact formula for the correlators of all pairwise identical operators, |
| title | Mellin amplitudes for $AdS_3 \times S^3$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.17420 |