Syzygies probing scattering amplitudes

被引：0
作者：
Gang Chen
Junyu Liu
Ruofei Xie
Hao Zhang
Yehao Zhou
机构：
[1] Zhejiang Normal University,Department of Physics
[2] Nanjing University,Department of Physics
[3] University of Science and Technology of China,School of the Gifted Young
[4] University of Science and Technology of China,School of Physical Sciences
来源：
Journal of High Energy Physics | / 2016卷
关键词：
Differential and Algebraic Geometry; Scattering Amplitudes;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We propose a new efficient algorithm to obtain the locally minimal generating set of the syzygies for an ideal, i.e. a generating set whose proper subsets cannot be generating sets. Syzygy is a concept widely used in the current study of scattering amplitudes. This new algorithm can deal with more syzygies effectively because a new generation of syzygies is obtained in each step and the irreducibility of this generation is also verified in the process. This efficient algorithm can also be applied in getting the syzygies for the modules. We also show a typical example to illustrate the potential application of this method in scattering amplitudes, especially the Integral-By-Part(IBP) relations of the characteristic two-loop diagrams in the Yang-Mills theory.
引用
收藏
相关论文
共 85 条
[1]  
Britto R(2005)Direct proof of tree-level recursion relation in Yang-Mills theory Phys. Rev. Lett. 94 181602-undefined
[2]  
Cachazo F(2004)Trees, parking functions, syzygies, and deformations of monomial ideals Trans. Amer. Math. Soc. 356 3109-undefined
[3]  
Feng B(2011)Towards a basis for planar two-loop integrals Phys. Rev. D 83 045012-undefined
[4]  
Witten E(2012)A new algorithm for the generation of unitarity-compatible integration by parts relations JHEP 01 077-undefined
[5]  
Postnikov A(2011)Integration by parts: an introduction Int. J. Mod. Phys. A 26 2807-undefined
[6]  
Shapiro B(2012)Maximal unitarity at two loops Phys. Rev. D 85 045017-undefined
[7]  
Gluza J(2016)Integration-by-parts reductions from unitarity cuts and algebraic geometry Phys. Rev. D 93 041701-undefined
[8]  
Kajda K(2015)On-shell structures of MHV amplitudes beyond the planar limit JHEP 06 179-undefined
[9]  
Kosower DA(2015)Non-planar on-shell diagrams JHEP 06 199-undefined
[10]  
Schabinger RM(2016)On-shell diagrams, Graßmannians and integrability for form factors JHEP 01 182-undefined
123456789