A Calabi-Yau-to-curve correspondence for Feynman integrals - Hans Jockers; Sören Kotlewski; Pyry Kuusela; Andrew J. McLeod; Sebastian Pögel; Maik Sarve; Xing Wang; Stefan Weinzierl (Journal of High Energy Physics)
Abstract It has long been known that the maximal cut of the equal-mass four-loop banana integral is a period of a family of Calabi-Yau threefolds that depends on the kinematic variable z = m 2/p 2. We show that it can also be interpreted as a period of a family of genus-two curves. We do this by introducing a general Calabi-Yau-to-curve correspondence, which in this case locally relates the original period of the family of Calabi-Yau threefolds to a period of a family of genus-two curves that varies holomorphically with the kinematic variable z. In addition to working out the concrete details of this correspondence for the equal-mass four-loop banana integral, we outline when we expect a correspondence of this type to hold.