The Eynard–Orantin recursion and equivariant mirror symmetry for the projective line

We study the equivariantly perturbed mirror Landau–Ginzburg model of [math] . We show that the Eynard–Orantin recursion on this model encodes all-genus, all-descendants equivariant Gromov–Witten invariants of [math] . The nonequivariant limit of this result is the Norbury–Scott conjecture, while by taking large radius limit we recover the Bouchard–Mariño conjecture on simple Hurwitz numbers.