$p$-adic Mellin Amplitudes

Christian Baadsgaard Jepsen; Sarthak Parikh

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arXiv · 1808.08333

$p$-adic Mellin Amplitudes

Christian Baadsgaard Jepsen·Sarthak Parikh

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Abstract

In this paper, we propose a $p$-adic analog of Mellin amplitudes for scalar operators, and present the computation of the general contact amplitude as well as arbitrary-point tree-level amplitudes for bulk diagrams involving up to three internal lines, and along the way obtain the $p$-adic version of the split representation formula. These amplitudes share noteworthy similarities with the usual (real) Mellin amplitudes for scalars, but are also significantly simpler, admitting closed-form expressions where none are available over the reals. The dramatic simplicity can be attributed to the absence of descendant fields in the $p$-adic formulation.

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Christian Baadsgaard Jepsen, Sarthak Parikh. 2018-08-24. $p$-adic Mellin Amplitudes. https://arxiv.org/abs/1808.08333

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