Algorithm for differential equations for Feynman integrals in general dimensions (Q6571070)

Feynman integrals are key ingredients in various areas of physics, and their accurate calculation, whether analytically or numerically, remains a significant hurdle in advancing our understanding of physical phenomena. In particular, identifying the specific types of special functions required to evaluate Feynman integrals has been an ongoing challenge since the early days of quantum field theory.\N\NThe authors present an analgorithm for determining the minimal order differential equations associated with a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted to the case of twisted differential forms. In dimensional regularisation, the author proves the applicability of this algorithm by explicitly providing the inhomogeneous differential equations for the multi-loop two-point sunset integrals: up to 20 loops for the equal mass case, the generic mass case at two- and three-loop orders. The authors derive the differential operators for various infrared-divergent two-loop graphs. In the analytic regularisation case, they apply the algorithm for deriving a system of partial differential equations for regulated Witten diagrams, which arise in the evaluation of cosmological correlators of conformally coupled \(\phi^4\) theory in four-dimensional de Sitter space.