2017/03/31 by Fei Teng, Bo Feng · 72 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Classical mechanics #Combinatorics #Cosmology and Gravitation Theories #Einstein #Formalism (music) #Gauge theory #Gluon #Gravitation #Graviton #Helicity #Kruskal's algorithm #Mathematical physics #Mathematics #Particle physics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Spacetime #Spanning tree #Yang–Mills existence and mass gap #hep-th
paper · pdf · doi:10.1007/jhep05(2017)075
published in Journal of High Energy Physics 2017(5) (Springer Nature) · 36 pages, 3 captioned figures; v2: more details added, revised and published version
openalex publication_date 2017/05/01 · arxiv created 2017/05/19 · arxiv updated 2017/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with an arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients.