One-loop integrand from generalised scattering equations

A bstract Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured ℂℙ k  − 1 , are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster algebras. Recently connections between one-loop integrands for bi-a...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2021; no. 5; pp. 1 - 42
Main Authors Abhishek, Md, Hegde, Subramanya, Saha, Arnab Priya
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 03.05.2021
Springer Nature B.V
SpringerOpen
Subjects
Algebra
Amplitudes
Classical and Quantum Gravitation
Clusters
Effective Field Theories
Elementary Particles
High energy physics
Kinematics
Physics
Physics and Astronomy
Polytopes
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scattering Amplitudes
String Theory
Effective Field Theories
Scattering Amplitudes
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Summary:A bstract Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured ℂℙ k  − 1 , are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster algebras. Recently connections between one-loop integrands for bi-adjoint cubic scalar theory and D n cluster polytope have been established. In this paper using the Gr (3 , 6) cluster algebra, we relate the singularities of (3 , 6) amplitude to four-point one-loop integrand in the bi-adjoint cubic scalar theory through the D 4 cluster polytope. We also study factorisation properties of the (3 , 6) amplitude at various boundaries in the worldsheet.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP05(2021)012