Speaker
Description
I will present the geometric integrand expansion, developed by Arkani-Hamed, Henn, and Trnka, for the pentagonal Wilson loop with a Lagrangian insertion in maximally supersymmetric Yang–Mills theory. The discussion will focus on integrated results corresponding to an all-loop class of ladder-type geometries, with particular emphasis on the two-loop observable examined through this geometric framework. We analytically evaluate the new two-loop integrals arising from the negative-geometry contribution using the canonical differential equations method. The analytic results reveal numerical evidence that each component exhibits uniform sign behaviour within the Amplituhedron region. Finally, I will report recent progress in bootstrapping ladder-type geometries via geometric Landau analysis, which identifies the physically relevant singularities of the integrals. This method successfully determines the symbol of the six-point two-loop and five-point three-loop ladder negative geometries, with the latter introducing novel pentagon alphabet letters also appearing in planar three-loop Feynman integrals.
