Toward the Feynman rule for n -point gluon Mellin amplitudes in AdS/CFT

We investigate the embedding formalism in conjunction with the Mellin transform to determine tree-level gluon amplitudes in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>AdS</a:mi><a:mo>/</a:mo><a:mi>CFT</a:mi></a:mrow></a:math>. 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>n</c:mi></c:math>-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. Published by the American Physical Society 2024