Gromov–Witten theory of K3 surfaces and a Kaneko–Zagier equation for Jacobi forms

Abstract

AbstractWe prove the existence of quasi-Jacobi form solutions for an analogue of the Kaneko–Zagier differential equation for Jacobi forms. The transformation properties of the solutions under the Jacobi group are derived. A special feature of the solutions is the polynomial dependence of the index parameter. The results yield an explicit conjectural description for all double ramification cycle integrals in the Gromov–Witten theory of K3 surfaces.