PIRSA:14020147

Cluster Polylogarithms for Scattering Amplitudes

(2014). Cluster Polylogarithms for Scattering Amplitudes. Perimeter Institute. https://pirsa.org/14020147

Cluster Polylogarithms for Scattering Amplitudes. Perimeter Institute, Feb. 18, 2014, https://pirsa.org/14020147 

          @misc{ pirsa_PIRSA:14020147,
            doi = {10.48660/14020147},
            url = {https://pirsa.org/14020147},
            author = {},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Cluster Polylogarithms for Scattering Amplitudes},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {feb},
            note = {PIRSA:14020147 see, \url{https://pirsa.org}}
          }
Talk number
PIRSA:14020147
Collection
Talk Type
Subject
Abstract

Motivated by the cluster structure of two-loop scattering amplitudes in N = 4 Yang-Mills theory we define cluster polylogarithm functions. We find that all such functions of weight 4 are made up of a single simple building block associated to the A2 cluster algebra. Adding the requirement of locality on generalized Stasheff polytopes, we find that these A2 building blocks arrange themselves to form a unique function associated to the A3 cluster algebra. ThisA3 function manifests all of the cluster algebraic structure of the two-loop n-particle MHV amplitudes for all n, and we use it to provide an explicit representation for the most complicated part of the n = 7 amplitude as an example.