Permutation in the CHY-Formulation

Understand

The CHY-integrand of bi-adjoint cubic scalar theory is a product of two PT-factors.

• This pair of PT-factors can be interpreted as defining a permutation.
• We introduce the cycle representation of permutation in this paper for the understanding of cubic scalar amplitude.
• We show that, given a permutation related to the pair of PT-factors, the pole and vertex information of Feynman diagrams of corresponding CHY-integrand is completely characterized by the cycle representation of permutation.