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arXiv · 2408.17420

Mellin amplitudes for $AdS_3 \times S^3$

Connor Behan·Rodrigo S. Pitombo
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Abstract

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,

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Connor Behan, Rodrigo S. Pitombo. 2025-02-05. Mellin amplitudes for $AdS_3 \times S^3$. https://doi.org/10.1007/jhep11(2024)059

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