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Planar matrices and arrays of Feynman diagrams

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Recently,planar collections of Feynman diagrams were proposed by Borges and one of the authors as the natural generalization of Feynman diagrams for the computation of k=3 biadjoint amplitudes.Planar collections are one-dimensional arrays of metric trees satisfying an induced planarity and compatibility condition.In this work,we introduce planar matrices of Feynman diagrams as the objects that compute k=4 biadjoint amplitudes.These are symmetric matrices of metric trees satisfying compatibility conditions.We introduce two notions of combinatorial bootstrap techniques for finding collections from Feynman diagrams and matrices from collections.As applications of the first,we find all 693,13 612 and 346 710 collections for(k,n)=(3,7),(3,8)and(3,9),respectively.As applications of the second kind,we find all 90 608 and 30 659 424 planar matrices that compute(k,n)=(4,8)and(4,9)biadjoint amplitudes,respectively.As an example of the evaluation of matrices of Feynman diagrams,we present the complete form of the(4,8)and(4,9)biadjoint amplitudes.We also start a study of higher-dimensional arrays of Feynman diagrams,including the combinatorial version of the duality between(k,n)and(n-k,n)objects.

Feynman diagramsbiadjoint amplitudestropical Grassmannian

Freddy Cachazo、Alfredo Guevara、Bruno Umbert、Yong Zhang

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Perimeter Institute for Theoretical Physics,Waterloo,ON N2L 2Y5,Canada

Department of Physics and Astronomy,University of Waterloo,Waterloo,ON N2L 3G1,Canada

CECs Valdivia y Departamento de Física,Universidad de Concepción,Casilla 160-C,Concepción,Chile

Center for the Fundamental Laws of Nature,Society of Fellows and Black Hole Initiative,Harvard University,Cambridge,MA 02138,United States of America

Department of Applied Mathematics,Western University,London,ON N6A 5B7,Canada

CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China

School of Physical Sciences,University of Chinese Academy of Sciences,No.19A Yuquan Road,Beijing 100049,China

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2024

10.1088/1572-9494/ad102d

理论物理通讯(英文版)
中国科学院理论物理研究所 中国物理学会

理论物理通讯(英文版)

CSTPCD
影响因子：0.333
ISSN：0253-6102
年,卷(期)：2024.76(3)
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