Mirror Symmetry for open r-spin invariants

Abstract

We show that a generating function for open r-spin enumerative invariants produces a universal unfolding of the polynomial x r . Further, the coordinates parametrizing this universal unfolding are flat coordinates on the Frobenius manifold associated to the Landau-Ginzburg model (C, x r ) via Saito-Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel [GKT22].