000012112 001__ 12112 000012112 005__ 20250218124801.0 000012112 02470 $$ahttps://doi.org/10.1103/PhysRevD.109.106003$$2doi 000012112 037__ $$aTEXTUAL 000012112 037__ $$bArticle 000012112 041__ $$aeng 000012112 245__ $$aToward the Feynman rule for $n$-point gluon Mellin amplitudes in $AdS/CFT$ 000012112 269__ $$a2024-05-02 000012112 336__ $$aArticle 000012112 520__ $$aWe investigate the embedding formalism in conjunction with the Mellin transform to determine tree-level gluon amplitudes in $AdS/CFT$. Detailed computations of three to five-point correlators are conducted, ultimately distilling what were previously complex results for five-point correlators into a more succinct and comprehensible form. We then proceed to derive a recursion relation applicable to a specific class of n-point gluon amplitudes. This relation is instrumental in systematically constructing amplitudes for a range of topologies. We illustrate its efficacy by specifically computing six to eight-point functions. Despite the complexity encountered in the intermediate steps of the recursion, the higher-point correlator is succinctly expressed as a polynomial in boundary coordinates, upon which a specific differential operator acts. Remarkably, we observe that these amplitudes strikingly mirror their counterparts in flat space, traditionally computed using standard Feynman rules. This intriguing similarity has led us to propose a novel dictionary: comprehensive rules that bridge AdS Mellin amplitudes with flat-space gluon amplitudes. 000012112 540__ $$a<p>Published by the American Physical Society under the terms of the <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a> license.</p> 000012112 542__ $$fCC BY 000012112 690__ $$aPhysical Sciences Division 000012112 691__ $$aPhysics 000012112 7001_ $$1https://orcid.org/0009-0000-6553-0748$$2ORCID$$aChu, Jinwei$$uUniversity of Chicago 000012112 7001_ $$1https://orcid.org/0000-0001-9455-4183$$2ORCID$$aKharel, Savan$$uUniversity of Chicago 000012112 773__ $$tPhysical Review D 000012112 8564_ $$93f9c6ee9-b9de-4e6f-a35e-478911807ec2$$ePublic$$s2087105$$uhttps://knowledge.uchicago.edu/record/12112/files/PhysRevD.109.106003.pdf 000012112 908__ $$aI agree 000012112 909CO $$ooai:uchicago.tind.io:12112$$pGLOBAL_SET 000012112 983__ $$aArticle