Cluster Polylogarithms for Scattering Amplitudes

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.

Event Type: 
Seminar
Collection/Series: 
Scientific Area(s): 
Event Date: 
Mardi, Février 18, 2014 - 14:00 to 15:30
Location: 
Time Room