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-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.