An etude on recursion relations and triangulations

An etude on recursion relations and triangulations

A bstract Following [ 1 ], we derive a recursion relation by applying a one-parameter deformation of kinematic variables for tree-level scattering amplitudes in bi-adjoint ϕ 3 theory. The recursion relies on properties of the amplitude that can be made manifest in the underlying kinematic associahed...

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Bibliographic Details
Published in:The journal of high energy physics Vol. 2019; no. 5; pp. 1 - 27
Main Authors: He, Song, Yang, Qinglin
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2019
Springer Nature B.V
SpringerOpen
Subjects:
Amplitudes
Apexes
Classical and Quantum Gravitation
Deformation
Differential and Algebraic Geometry
Elementary Particles
High energy physics
Kinematics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scattering Amplitudes
String Theory
Triangulation
Scattering Amplitudes
Differential and Algebraic Geometry
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Summary:A bstract Following [ 1 ], we derive a recursion relation by applying a one-parameter deformation of kinematic variables for tree-level scattering amplitudes in bi-adjoint ϕ 3 theory. The recursion relies on properties of the amplitude that can be made manifest in the underlying kinematic associahedron, and it provides triangulations for the latter. Furthermore, we solve the recursion relation and present all-multiplicity results for the amplitude: by reformulating the associahedron in terms of its vertices, it is given explicitly as a sum of “volume” of simplicies for any triangulation, which is an analogy of BCFW representation/triangulation of amplituhedron for N = 4 SYM.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP05(2019)040