Seminar series
Date
Tue, 23 Mar 2021
16:00
16:00
Speaker
Aidan Herderschee
Organisation
University of Michigan
I will give an introduction to the connection between the positive kinematic region and the analytic structure of integrated amplitudes in $\mathcal{N}=4$ SYM at all loop orders. I will first review known results for 6-point and 7-point amplitudes and how cluster algebras provide a very precise understanding of the positive kinematic region. I will then move onto 8-point amplitudes, where a number of phenomena appear not suited to the cluster algebra framework. For example, logarithmic branch points associated with algebraic functions appear at two loops in the 8-point NMHV amplitude. I argue that wall-crossing is a good framework to systematically study these algebraic branch points. Wall crossing has appeared in a number of research areas, most notably in study of moduli spaces of $\mathcal{N}=2$ gauge theories and the BDS ansatz. In the context of $\mathcal{N}=4$ SYM, we see that wall crossing provides a new way to systematically study the boundary structure of the positive kinematic region. I conclude with a list of results for the 8-point amplitude.
This talk will focus mostly on Sections 1 and 2 of 2102.03611. I will give a brief summary of Section 3 at the end of the talk