The spin Gromov–Witten/Hurwitz correspondence for \({\mathbb{P}}^1\)

We study the spin Gromov–Witten theory of \(\mathbb{P}^1\). Using the standard torus action on \(\mathbb{P}^1\), we prove that the associated equivariant potential can be expressed by means of operator formalism and satisfies the 2-BKP hierarchy. As a consequence of this result, we prove the spin analogue of the Gromov–Witten/Hurwitz correspondence of Okounkov–Pandharipande for \(\mathbb{P}^1\), which was conjectured by J. Lee. Finally, we prove that this correspondence for a general target spin curve follows from a conjectural degeneration formula for spin Gromov–Witten invariants that holds in virtual dimension 0.