Elliptic Virtual Structure Constants and Generalizations of BCOV-Zinger Formula to Projective Fano Hypersurfaces

In this paper, we propose a recipe for B-model computation of genus 1 Gromov-Witten invariants of Calabi-Yau and Fano Projective Hypersurfaces. Our formalism can be applied equally to both Calabi-Yau and Fano cases. In the Calabi-Yau case, drastic cancellation of terms used in our formalism occurs and it results in another representation of BCOV-Zinger formula for projective Calabi-Yau hypersurfaces.
Comment: 26pages, 8 figures, minor errors are corrected, figures are refined, errors in reference list are corrected, linguistic errors are corrected. revised version for submission to JHEP