{
  "id": "2108.01410",
  "version": "v1",
  "published": "2021-08-03T10:58:32.000Z",
  "updated": "2021-08-03T10:58:32.000Z",
  "title": "Cohen-Macaulay Property of Feynman Integrals",
  "authors": [
    "Felix Tellander",
    "Martin Helmer"
  ],
  "categories": [
    "hep-th",
    "math-ph",
    "math.AG",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-03T10:58:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "feynman integrals",
      "cohen-macaulay property",
      "hypergeometric system",
      "computational tools",
      "series representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}