Shruti Paranjape | Loops in a loop expansion 

Amplituhedra, Cluster Algebras, and Positive Geometry Conference
May 31, 2024
Speaker: Shruti Paranjape, UC Davis
Title: Loops in a loop expansion
Abstract: In a paper by Arkani-Hamed, Henn and Trnka, it was shown that the amplituhedron construction of N=4 SYM can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momentum twistors. Furthermore, using differential equation methods, it was possible to calculate and resum integrated expressions and obtain strong coupling results. In this talk, we provide a more general framework for the loops of loops expansion and outline a powerful method for the determination of differential forms for higher-order geometries. In particular, we will focus on the case of 1 closed cycle in loop space and select integrated results.