Mirror Symmetry for open r-spin invariants

TL;DR

This paper demonstrates that the generating function for open r-spin invariants creates a universal unfolding of the polynomial x^r, linking it to Frobenius manifold structures and suggesting broader applicability in higher dimensions.

Contribution

It establishes a connection between open r-spin invariants and Frobenius manifolds, showing the generating function forms a universal unfolding of x^r and providing evidence for higher-dimensional generalizations.

Findings

Generating function produces a universal unfolding of x^r

Coordinates are flat on the associated Frobenius manifold

Supports conjecture of similar phenomena in higher dimensions

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 a sequel paper.