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

Jinwei Chu (Department of Physics, University of Chicago, Chicago, Illinois 60637, USA) ; Savan Kharel (Department of Physics, University of Chicago, Chicago, Illinois 60637, USA)

We 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.

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      "title": "Toward the Feynman rule for <math><mi>n</mi></math>-point gluon Mellin amplitudes in <math><mrow><mi>AdS</mi><mo>/</mo><mi>CFT</mi></mrow></math>"
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Published on:
02 May 2024
Publisher:
APS
Published in:
Physical Review D , Volume 109 (2024)
Issue 10
DOI:
https://doi.org/10.1103/PhysRevD.109.106003
arXiv:
2401.00038
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: