Cluster algebraic structures in Feynman integrals

Ömer Gürdoğan (U Southampton)

Mar 12. 2026, 09:30 — 10:30

For a long time the symbol letters of amplitudes and Feynman integrals, ie their branch points and of their discontinuities, have been observed to obey cluster exchange relations. In some cases, eg six- and seven- particle scattering in planar N=4 super Yang-Mills, this is a very convincing observation that is verified to very high loop orders. Other quantities, such as form factors, QCD amplitudes, and individual Feynman integrals have been found to “mostly" obey exchange relations without a clear cluster algebra behind them. In all cases, this has been an observation without a clear explanation. I will provide an overview of the current status of the cluster-algebraic observations around the symbol letters of amplitudes, and I will speculate on the relevance of resurgent analysis as a potential tool to explain these structures.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Amplitudes and Algebraic Geometry (Thematic Programme)
Organizer(s):
Daniele Agostini (U Tübingen)
Lara Bossinger (UNAM, Oaxaca)
Ruth Britto (Trinity College, Dublin)
Johannes Henn (MPP, Munich)
Jianrong Li (U of Vienna)
Anna-Laura Sattelberger (MPI MIS, Leipzig)
Oliver Schlotterer (Uppsala U)