期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 4, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP04(2021)002
关键词
Differential and Algebraic Geometry; Scattering Amplitudes
资金
- ERC [648630 IQFT]
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [724638]
In this paper, we discuss the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. The tropical fans discussed in this study not only generate natural finite sets of letters, but also provide letters containing square roots, with the minimal fan considered providing all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.
We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.
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