Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-03-30
Nucl.Phys.B429:626-674,1994
Physics
High Energy Physics
High Energy Physics - Theory
57 pages + 9 figures using epsf
Scientific paper
10.1016/0550-3213(94)90155-4
We describe in detail the space of the two K\"ahler parameters of the Calabi--Yau manifold $\P_4^{(1,1,1,6,9)}[18]$ by exploiting mirror symmetry. The large complex structure limit of the mirror, which corresponds to the classical large radius limit, is found by studying the monodromy of the periods about the discriminant locus, the boundary of the moduli space corresponding to singular Calabi--Yau manifolds. A symplectic basis of periods is found and the action of the $Sp(6,\Z)$ generators of the modular group is determined. From the mirror map we compute the instanton expansion of the Yukawa couplings and the generalized $N=2$ index, arriving at the numbers of instantons of genus zero and genus one of each degree. We also investigate an $SL(2,\Z)$ symmetry that acts on a boundary of the moduli space.
Candelas Philip
Font Anamaria
Katz Sheldon
Morrison David R.
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