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arXiv · 2108.01410

Cohen-Macaulay Property of Feynman Integrals

Felix Tellander·Martin Helmer
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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.

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Felix Tellander, Martin Helmer. 2021-08-03. Cohen-Macaulay Property of Feynman Integrals. https://doi.org/10.1007/s00220-022-04569-6

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