Abstract
We explore the use of the differential representation of AdS amplitudes to compute Witten diagrams. The differential representation expresses AdS amplitudes in terms of conformal generators acting on contact Witten diagrams, which allows us to construct differential equations for Witten diagrams. These differential equations can then be transformed into difference equations in Mellin space, which can be solved recursively. Using this method, we efficiently re-computed scalar four-point amplitudes and obtained new results for scalar six-point amplitudes mediated by gluons and scalars, as well as two examples of scalar eight-point amplitudes from gluon exchange.
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Acknowledgments
We thank Agnese Bissi, Simon Caron-Huot, Arthur Lipstein, Julio Parra-Martinez, Charlotte Sleight, David Simmons-Duffin for useful discussions. We are also grateful to Fei Teng and Xinan Zhou for valuable comments on the draft. YZL is supported by the Simons Foundation through the Simons Collaboration on the Nonperturbative Bootstrap. JM is supported by a Durham-CSC Scholarship.
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Li, YZ., Mei, J. Bootstrapping Witten diagrams via differential representation in Mellin space. J. High Energ. Phys. 2023, 156 (2023). https://doi.org/10.1007/JHEP07(2023)156
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DOI: https://doi.org/10.1007/JHEP07(2023)156