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 $(\mathbb{C}, x^r)$ via Saito–Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel $\href{https://arxiv.org/abs/2203.02435}{[\textrm{GKT}22]}$.