https://doi.org/10.1140/epjc/s10052-022-11168-1
Regular Article - Theoretical Physics
The KLT relation from the tree formula and permutohedron
Department of Physics, Zhejiang Institute of Modern Physics, Zhejiang University, 310027, Hangzhou, China
Received:
13
September
2022
Accepted:
23
December
2022
Published online:
27
January
2023
In this paper, we generalize the Nguyen–Spradlin–Volovich–Wen (NSVW) tree formula from the MHV sector to any helicity sector. We find a close connection between the Permutohedron and the KLT relation, and construct a non-trivial mapping between them, linking the amplitudes in the gauge and gravity theories. The gravity amplitude can also be mapped from a determinant followed from the matrix-tree theorem. Besides, we use the binary tree graphs to manifest its Lie structure. In our tree formula, there is an evident Hopf algebra of the permutation group behind the gravity amplitudes. Using the tree formula, we can directly re-derive the soft/collinear limit of the amplitudes.
© The Author(s) 2023
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