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  • Open Access

Hidden Simplicity in AdS Spinning Mellin Amplitudes via Scaffolding

Song He (何颂)1,2,3,4,*, Xiang Li (李想)2,3,†, Yuyu Mo (莫裕宇)2,‡, and Dongyu Yang (杨东昱)1,2,3,§

  • *Contact author: songhe@itp.ac.cn
  • †Contact author: lixiang@itp.ac.cn
  • ‡Contact author: moyuyu@itp.ac.cn
  • §Contact author: yangdongyu24@mails.ucas.ac.cn
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Phys. Rev. Lett. 137, 161602 – Published 14 October, 2026

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

Abstract

We uncover surprising hidden simplicity in Mellin amplitudes for tree-level anti–de Sitter (AdS) holographic correlators for AdS “gluon” (spin-1) operators. We define Mellin amplitudes with n spinning operators via the so-called scaffolding 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 them 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, multilinearity, 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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Phys. Rev. Lett. 137, 161602– Published 14 October, 2026
  • Received 27 April 2026
  • Accepted 10 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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