THE SPIN GROMOV–WITTEN/HURWITZ CORRESPONDENCE FOR P^1

We study the spin Gromov–Witten (GW) theory of P1. Using the standard torus action on P1, 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 GW/Hurwitz correspondence of Okounkov–Pandharipande for P1, 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 GW invariants that holds in virtual dimension 0