Mirror equivalence of higher-genus BCOV and Gromov–Witten invariants

Establish the equivalence between all higher-genus BCOV invariants on compact Calabi–Yau manifolds and all higher-genus Gromov–Witten invariants on the mirror Calabi–Yau manifolds.

Background

The paper constructs perturbative quantum BCOV invariants on arbitrary compact Calabi–Yau manifolds by providing an explicit quantization that includes descendant fields and all loop orders. It states that these invariants are expected to correspond, under mirror symmetry, to higher-genus Gromov–Witten invariants of the mirror manifolds. The claimed equivalence is not established in this paper; the paper only notes that it was previously proved for elliptic curves.