2019/12/31 by Aidan Herderschee, Song He, Fei Teng +1 · 12 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Canonical form #Cosmology and Gravitation Theories #Duality (order theory) #Fundamental representation #Noncommutative and Quantum Gravity Theories #Polytope #Scalar (mathematics) #Scattering #Scattering amplitude #Wedge (geometry) #hep-th #math.CO
paper · pdf · doi:10.1007/jhep06(2020)030
published in Journal of High Energy Physics 2020(6) (Springer Nature) · 47 pages and 9 figures; v2: more references added and typos corrected; v3: published version and typos corrected
openalex created_date 2019/12/26 · openalex publication_date 2020/06/03 · arxiv created 2020/06/05 · arxiv updated 2020/06/08 · openalex updated_date 2026/08/05
A bstract We initiate the study of positive geometry and scattering forms for tree- level amplitudes with matter particles in the (anti-)fundamental representation of the color/flavor group. As a toy example, we study the bi-color scalar theory, which supplements the bi-adjoint theory with scalars in the (anti-)fundamental representations of both groups. Using a recursive construction we obtain a class of unbounded polytopes called open associahedra (or associahedra with certain facets at infinity) whose canonical form computes amplitudes in bi-color theory, for arbitrary number of legs and flavor assignments. In addition, we discuss the duality between color factors and wedge products, or “color is kinematics”, for amplitudes with matter particles as well.