Journal of High Energy Physics ( IF 5.4 ) Pub Date : 2021-05-03 , DOI: 10.1007/jhep05(2021)012 Md. Abhishek , Subramanya Hegde , Arnab Priya Saha
Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured ℂℙk − 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 \( {\mathcal{D}}_n \) 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 \( {\mathcal{D}}_4 \) cluster polytope. We also study factorisation properties of the (3, 6) amplitude at various boundaries in the worldsheet.
A preprint version of the article is available at ArXiv.中文翻译:
广义散射方程的一环积分
从k − 1的模空间上的积分获得的广义双伴随标量幅值是CHY形式论的新扩展。这些幅度具有格拉斯曼簇代数的实现。最近,已经建立了用于双伴随三次标量理论的单环积分与\({{mathcal {D}} _ n \)簇多面体之间的联系。在使用GR这纸(3 , 6)簇代数,我们涉及的奇点(3 , 6)振幅通过在双伴随立方标量理论四点一环积\({\ mathcal {d }} _ 4 \)集群多面体。我们还研究了(3 , 6)在世界范围内的各种边界处的振幅。
该文章的预印本可在ArXiv上获得。