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BCJ numerators from reduced Pfaffian

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arxiv 1703.05717 v1 pith:AVAP72JM submitted 2017-03-16 hep-th

BCJ numerators from reduced Pfaffian

Yi-Jian Du , Fei Teng This is my paper
classification hep-th
keywords numeratorsnlsmpfaffianreducedcorrespondingformnumberrules
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the Bern-Carrasco-Johansson (BCJ) numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensions. In this work, we give a set of very straightforward graphic rules based on spanning trees for a direct evaluation of the BCJ numerators for YM and NLSM. Such rules can be derived from the Laplace expansion of the corresponding reduced Pfaffian. For YM, the each one of the $(n-2)!$ DDM form BCJ numerators contains exactly $(n-1)!$ terms, corresponding to the increasing trees with respect to the color order. For NLSM, the number of nonzero numerators is at most $(n-2)!-(n-3)!$, less than those of several previous constructions.

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Cited by 12 Pith papers

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