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arXiv · 1702.05840

Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism

Rijun Huang·Yi-Jian Du·Bo Feng
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Abstract

For a physical field theory, the tree-level amplitudes should possess only single poles. However, when computing amplitudes with Cachazo-He-Yuan (CHY) formulation, individual terms in the intermediate steps will contribute higher-order poles. In this paper, we investigate the cancelation of higher-order poles in CHY formula with Pfaffian as the building block. We develop a diagrammatic rule for expanding the reduced Pfaffian. Then by organizing diagrams in appropriate groups and applying the cross-ratio identities, we show that all potential contributions to higher-order poles in the reduced Pfaffian are canceled out, i.e., only single poles survive in Yang-Mills theory and gravity. Furthermore, we show the cancelations of higher-order poles in other field theories by introducing appropriate truncations, based on the single pole structure of Pfaffian.

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Rijun Huang, Yi-Jian Du, Bo Feng. 2017-03-24. Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism. https://doi.org/10.1007/jhep06(2017)133

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