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High Energy Physics - Theory

arXiv:2108.01410 (hep-th)
[Submitted on 3 Aug 2021 (v1), last revised 2 May 2022 (this version, v3)]

Title:Cohen-Macaulay Property of Feynman Integrals

Authors: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.
Comments: Clarified some of the technical aspects of the paper and added an appendix by Uli Walther. Also fixed typos
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Algebraic Geometry (math.AG)
Cite as: arXiv:2108.01410 [hep-th]
  (or arXiv:2108.01410v3 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2108.01410
Related DOI: https://doi.org/10.1007/s00220-022-04569-6

Submission history

From: Martin Helmer [view email]
[v1] Tue, 3 Aug 2021 10:58:32 UTC (31 KB)
[v2] Sun, 24 Apr 2022 18:06:46 UTC (34 KB)
[v3] Mon, 2 May 2022 17:51:34 UTC (34 KB)
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