• Accepted Paper

Hidden simplicity in AdS spinning Mellin amplitudes via scaffolding

Song He, Xiang Li, Yuyu Mo, and Dongyu Yang

Phys. Rev. Lett. - Accepted 10 September, 2026

DOI: https://doi.org/10.1103/2dww-769m

Abstract

We uncover surprising hidden simplicity in Mellin amplitudes for tree-level AdS holographic correlators for AdS gluon'' (spin 1) operators. We define Mellin amplitudes with $n$ spinning operators via the so-calledscaffolding’’ of 2n-scalar ones with specific projection operators for each spin state, which are rational functions of Mellin variables of 2n scalars generalizing flat-space scaffolding amplitudes. We classify possible three-point structures with spin 1 which take the same form as massive three-point amplitudes in flat space, and match with special solutions such as those extracted from 6-scalar ones in AdS5×S3. Focusing on AdS5 gluons, we directly bootstrap spinning amplitudes in scaffolding form up to n=6 gluons (which amounts to 2n=12 scalars) using factorizations, multi-linearity and flat-space limit. The results take a remarkably simple form in analogy with flat-space amplitudes, which can be constructed from familiar 3- and 4-vertices as well as propagators of massive spin-1 particles. Surprisingly, we find that vertices with any descendant levels are proportional to the primary ones with nice combinatorial coefficients, which makes manifest the correct flat-space limit in the simplest possible way.

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