Journal of High Energy Physics (Oct 2020)

Symbol alphabets from plabic graphs

  • Jorge Mago,
  • Anders Schreiber,
  • Marcus Spradlin,
  • Anastasia Volovich

DOI
https://doi.org/10.1007/JHEP10(2020)128
Journal volume & issue
Vol. 2020, no. 10
pp. 1 – 17

Abstract

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Abstract Symbol alphabets of n-particle amplitudes in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory are known to contain certain cluster variables of Gr(4, n) as well as certain algebraic functions of cluster variables. In this paper we suggest an algorithm for computing these symbol alphabets from plabic graphs by solving matrix equations of the form C ∙ Z = 0 to associate functions on Gr(m, n) to parameterizations of certain cells of Gr(k, n) indexed by plabic graphs. For m = 4 and n = 8 we show that this association precisely reproduces the 18 algebraic symbol letters of the two-loop NMHV eight-particle amplitude from four plabic graphs.

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