Cohen-Macaulay Property of Feynman Integrals

Journal article

Abstract The connection between Feynman integrals and GKZ A -hypergeometric systems has been a topic of recent interest with advances in mathematical techniques and computational tools opening new possibilities; in this paper we continue to explore this connection. To each such hypergeometric system there is an associated toric ideal, we prove that the latter has the Cohen-Macaulay property for two large families of Feynman integrals. This implies, for example, that both the number of independent solutions and dynamical singularities are independent of space-time dimension and generalized propagator powers. Furthermore, in particular, it means that the process of finding a series representation of these integrals is fully algorithmic.

Authors: Tellander, F; Helmer, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Communications in Mathematical Physics
• Volume: 399
• Issue: 2
• Publication date: 2022-12-10
• DOI: 10.1007/s00220-022-04569-6
• EISSN: 1432-0916
• ISSN: 0010-3616
• Language: English
• Keywords: Hypergeometric distribution; Propagator; Complex system; Representation; Feynman integral