Cluster Bootstrap for Seven-Particle Amplitudes and a Quiver Construction for Form Factor Alphabets

by Jiahao Liu (Institute of Theoretical Physics, Beijing)

Wednesday 29 Apr 2026, 11:00 → 12:00 Europe/Berlin

A.1.01 - Alps Süd (MPP)

In the past decade, significant efforts have been devoted to the symbol bootstrap program in planar N=4 super-Yang-Mills theory. A key insight is that symbol alphabets originate from cluster algebras, while the constraints — such as integrability, (extended) Steinmann relations and first/last entry conditions — are also encoded in the cluster language. We will revisit the symbol bootstrap for seven-particle MHV and NMHV amplitudes, where the alphabet is associated with the E₆ cluster algebra. By determining the five-loop result, we find that all coefficients are integers, and certain words exhibit recurrent patterns. While the cluster structure for amplitudes is by now well explored, a natural question is whether other physical observables admit similar structures. Motivated by recent bootstrap results for the four-point MHV tr(\phi^2) form factor, we propose that the symbol letters — including algebraic ones — can be obtained from a G(4,8) quiver via the folding procedure.