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Planar matrices and arrays of Feynman diagrams:poles for higher k
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Planar arrays of tree diagrams were introduced as a generalization of Feynman diagrams that enable the computation of biadjoint amplitudes mn(k)for k＞2.In this follow-up work,we investigate the poles ofmn(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 △k,n and rays in the tropical Grassmannian Tr(k,n).
Feynman diagramsbiadjoint amplitudespoles
Alfredo Guevara、Yong Zhang
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Perimeter Institute for Theoretical Physics,Waterloo,ON N2L 2Y5,Canada
Department of Physics & Astronomy,University of Waterloo,Waterloo,ON N2L 3G1,Canada
Society of Fellows,Harvard University,Cambridge,MA 02138,United States of America
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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Government of Canada through the Department of Innovation,Science and Economic Development CanadaProvince of Ontario through the Ministry of Economic Development,Job Creation and Trade
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