Genus-0 mirror equivalence via virtual structure constants (JS1 Conjecture)

Establish that for every non-singular degree k hypersurface M_N^k and all indices a,b, the perturbed two-point genus-0 Gromov–Witten generating function ⟨O_{h^a} O_{h^b}⟩_0(t^0,t^1,…,t^{N−2}) equals the B-model two-point virtual structure constant generating function w(O_{h^a} O_{h^b})_0(x^0(t^*),x^1(t^*),…,x^{N−2}(t^*)), where x^p(t^*) is the inverse of the mirror map defined from multi-point virtual structure constants.

Background

The paper revisits a conjecture originally proposed in JS1 relating A-model genus-0 Gromov–Witten invariants to B-model virtual structure constants through a mirror map constructed from multi-point virtual structure constants. The authors define the perturbed two-point genus-0 Gromov–Witten generating function and the corresponding B-model quantity, then state the conjectural equality after applying the inverse mirror map.

This conjecture aims to provide a computational pathway for genus-0 Gromov–Witten invariants using residue integrals on moduli spaces of quasimaps, leveraging the simpler geometry of these moduli spaces compared to stable maps. It has been numerically tested for low degrees in multiple examples, but a general proof is not provided in the paper.