English

Three Point Functions on the Sphere of Calabi-Yau d-Folds

High Energy Physics - Theory 2009-10-28 v2

Abstract

Using mirror symmetry in Calabi-Yau manifolds M, three point functions of A(M)-model operators on the genus 00 Riemann surface in cases of one-parameter families of dd-folds realized as Fermat type hypersurfaces embedded in weighted projective spaces and a two-parameter family of dd-fold embedded in a weighted projective space \amb{\amb} are studied. These three point functions \corrOa(1)Ob(l1)Oc(dl){\corr{\,{{\cal O}^{(1)}_{a}}\, {{\cal O}^{(l-1)}_{b}}\, {{\cal O}^{(d-l)}_{c}}\, }} are expanded by indeterminates ql{q_l}=e2πitl{e^{2\pi i {t_l}}} associated with a set of {\kae} coordinates {tl}\{{t_l}\} and their expansion coefficients count the number of maps. From these analyses, we can read fusion structure of Calabi-Yau A(M)-model operators. In our cases they constitute a subring of a total quantum cohomology ring of the A(M)-model operators. In fact we switch off all perturbation operators on the topological theories except for marginal ones associated with {\kae} forms of M. For that reason, the charge conservation of operators turns out to be a classical one.

Keywords

Cite

@article{arxiv.hep-th/9504114,
  title  = {Three Point Functions on the Sphere of Calabi-Yau d-Folds},
  author = {Katsuyuki Sugiyama},
  journal= {arXiv preprint arXiv:hep-th/9504114},
  year   = {2009}
}

Comments

22 pages, LaTex file