Project Details
Projekt
Feynman integrals, Calabi-Yau motives and their extensions
Applicant
Professor Albrecht Klemm, Ph.D.
Subject Area
Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
Term
since 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 508889767
This project aims at understanding key analytic and automorphic properties of multi-loop Feynman integrals occurring in a wide variety of computations in quantum field theory and gravitational systems. These computations give rise to iterated integrals of special functions associated to Calabi-Yau (CY) motives (CYM) and their extensions. The tools developed in the interdisciplinary effort between mathematics and physics to understand string theory are crucial in this context. In particular, it was observed that certain aspects of the theory of variations of the mixed Hodge structure and the symplectic structure of CY varieties, developed to understand Categorical Mirror Symmetry, and the enormous databases of deformation families of CY and Fano varieties and their topological data, collected to classify string vacua, have become indispensable tools to uncover the analytic properties of higher-loop Feynman integrals. It is the goal of this project to extend this exciting interdisciplinary development to include further properties of CYMs, e.g., the finer integer enumerative invariants associated to the automorphic properties of the families of the motives, the relation of the flat Gauss-Manin connection to integrable systems, the representation-theoretic aspects of their monodromy groups and their fibrewise automorphic properties encoded in the Hasse-Weil Zeta function, obtained by Dwork’s p-adic deformation method. This project plays a central role in the proposed Research Unit, as it studies and develops mathematical tools needed to understand the special functions and iterated integrals that arise from multi-loop Feynman integrals, both in the context of the Research Unit and beyond.
DFG Programme
Research Units
Subproject of
FOR 5582:
Modern Foundations of Scattering Amplitudes
