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

Abstract

Using mirror symmetry in Calabi-Yau manifolds M, three point functions of A(M)-model operators on the genus $0$ Riemann surface in cases of one-parameter families of $d$-folds realized as Fermat type hypersurfaces embedded in weighted projective spaces and a two-parameter family of $d$-fold embedded in a weighted projective space ${\amb}$ are studied. These three point functions ${\corr{\,{{\cal O}^{(1)}_{a}}\, {{\cal O}^{(l-1)}_{b}}\, {{\cal O}^{(d-l)}_{c}}\, }}$ are expanded by indeterminates $q_l$=$e^{2\pi i{t}_l}$ associated with a set of {\kae} coordinates $\{t_l\}$ 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.

22 pages, LaTex file

References in corpus (3)

• Mirror Manifolds And Topological Field Theory
• Mirror Manifolds in Higher Dimension
• Mirror Symmetry and An Exact Calculation of N-2 Point Correlation Function on Calabi-Yau Manifold embedded in CP^{N-1}

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• Disk Amplitudes in Topological A-Model on Calabi-Yau Spaces and Fano Manifolds
• Kähler Potential of Moduli Space of Calabi-Yau $d$-fold embedded in $C{P}^{d+1}$
• Genus One Partition Function of the Calabi-Yau d-Fold embedded in $C{P}^{d+1}$