Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity
Freddy Cachazo, Nick Early, and Yong Zhang
Contact the author: Please use for correspondence this email.
Submission date: 06. Apr. 2023
Download full preprint: PDF (1031 kB)
Link to arXiv: See the arXiv entry of this preprint.
The biadjoint scalar theory has cubic interactions and ﬁelds transforming in the biadjoint representation of SU(N) × SU(Ñ). Amplitudes are “color” decomposed in terms of partial amplitudes computed using Feynman diagrams which are simultaneously planar with respect to two orderings. In 2019, a generalization of biadjoint scalar amplitudes based on generalized Feynman diagrams (GFDs) was introduced. GFDs are collections of Feynman diagrams derived by incorporating an additional constraint of “local planarity” into the construction of the arrangements of metric trees in combinatorics. In this work we propose a natural generalization of color orderings which leads to color-dressed amplitudes. A generalized color ordering is deﬁned as a collection of standard color orderings that is induced, in a precise sense, from an arrangement of projective lines on ℝℙ2. We present results for n ≤ 9 generalized color orderings and GFDs, uncovering new phenomena in each case. We discover generalized decoupling identities and propose a deﬁnition of the “colorless” generalized scalar amplitude. We also give a preview of a companion paper introducing new objects called chirotopal tropical Grassmannians, their connection to generalized color orderings, and to CEGM integral formulas.