Planar matrices and arrays of Feynman diagrams:poles for higher k  

作　　者：Alfredo Guevara Yong Zhang 

机构地区：[1]Perimeter Institute for Theoretical Physics,Waterloo,ON N2L 2Y5,Canada [2]Department of Physics&Astronomy,University of Waterloo,Waterloo,ON N2L 3G1,Canada [3]Society of Fellows,Harvard University,Cambridge,MA 02138,United States of America [4]CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China [5]School of Physical Sciences,University of Chinese Academy of Sciences,No.19A Yuquan Road,Bejing 100049,China

出　　处：《Communications in Theoretical Physics》2024年第4期1-13,共13页理论物理通讯（英文版）

基　　金：supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada;by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade

摘　　要：Planar arrays of tree diagrams were introduced as a generalization of Feynman diagrams that enable the computation of biadjoint amplitudes m_(n)(^(k))for k>2.In this follow-up work,we investigate the poles of m_(n)(^(k))from the perspective of such arrays.For general k,we characterize the underlying polytope as a Flag Complex and propose a computation of the amplitude-based solely on the knowledge of the poles,whose number is drastically less than the number of the full arrays.As an example,we first provide all the poles for the cases(k,n)=(3,7),(3,8),(3,9),(3,10),(4,8)and(4,9)in terms of their planar arrays of degenerate Feynman diagrams.We then implement simple compatibility criteria together with an addition operation between arrays and recover the full collections/arrays for such cases.Along the way,we implement hard and soft kinematical limits,which provide a map between the poles in kinematic space and their combinatoric arrays.We use the operation to give a proof of a previously conjectured combinatorial duality for arrays in(k,n)and(n-k,n).We also outline the relation to boundary maps of the hypersimplex Δ_(k,n) and rays in the tropical Grassmannian Tr(k,n).

关 键 词：Feynman diagrams biadjoint amplitudes POLES 

分 类 号：O411.1[理学—理论物理]