TY - JOUR

T1 - Mirror symmetry for two-parameter models - II

AU - Candelas, Philip

AU - Font, Anamaría

AU - Katz, sheldon

AU - Morrison, David R.

N1 - Funding Information:
Supported in part by the Robert A. Welch Foundation, NSF grants PHY-9009850, DMS-9311386 and DMS-9304580, and an American Mathematical Society Centennial Fellowship.

PY - 1994/11/7

Y1 - 1994/11/7

N2 - We describe in detail the space of the two Kähler parameters of the Calabi-Yau manifold P4(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 thes genralized N = 2 index, arriving at them numbers of instantons of genus zero and genus one of each bidegree. We find that these numbers can be negative, even in genus zero. We also investigate an SL(2, Z) symmetry that acts on a boundary of the moduli space.

AB - We describe in detail the space of the two Kähler parameters of the Calabi-Yau manifold P4(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 thes genralized N = 2 index, arriving at them numbers of instantons of genus zero and genus one of each bidegree. We find that these numbers can be negative, even in genus zero. We also investigate an SL(2, Z) symmetry that acts on a boundary of the moduli space.

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U2 - 10.1016/0550-3213(94)90155-4

DO - 10.1016/0550-3213(94)90155-4

M3 - Article

AN - SCOPUS:0001165006

VL - 429

SP - 626

EP - 674

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -