One-loop integrand from generalised scattering equations

Abstract 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-adjo...

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Bibliographic Details
Main Authors: Md. Abhishek, Subramanya Hegde, Arnab Priya Saha
Format: Article
Language:English
Published: SpringerOpen 2021-05-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP05(2021)012
Description
Summary:Abstract 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 $$ {\mathcal{D}}_n $$ 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 $$ {\mathcal{D}}_4 $$ cluster polytope. We also study factorisation properties of the (3, 6) amplitude at various boundaries in the worldsheet.
ISSN:1029-8479