DESY/Hamburg U. String Theory Seminar

Scattering amplitudes, Feynman integrals and cluster algebras

by Song He (Chinese Academy of Sciences)


I will review some observations based on new computations of multi-loop, multi-leg scattering amplitudes/Wilson loops in planar N=4 SYM, as well as for a class of Feynman integrals to all loops. The symbols of such amplitudes and integrals exhibit remarkable structures related to certain cluster algebras, extending those observed in the hexagon/heptagon bootstrap. We find the symbol alphabets for all these cases to be finite-type cluster algebras or truncated version of infinite cluster algebras, and they respect the so-called extended Steinmann relations (or cluster adjacency) universally. These conjectural all-loop structures may provide insights into properties of amplitudes and integrals in general QFT.