Quantum geometry of elliptic Calabi-Yau manifolds
Quantum geometry of elliptic Calabi-Yau manifolds
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DOI：
10.4310/cntp.2012.v6.n4.a5
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发表时间：
2012-05
影响因子：
1.9
通讯作者：
A. Klemm;J. Manschot;Thomas Wotschke
中科院分区：
文献类型：
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作者：
A. Klemm;J. Manschot;Thomas Wotschke
我们研究了Calabi-Yau三叠体的量子几何，它们是二维Toric基上的椭圆体。给出了拓扑弦自由能的全纯反常方程，该方程在亏格展开和基曲线类中都是迭代的。BRE上的T-对偶意味着拓扑弦自由能也捕捉到包裹椭圆BRE的D4-膜和基中的一个类的BPS不变量。我们通过显式计算有理椭圆曲面上3D4膜的BPS不变量来验证这一结论。
We study the quantum geometry of the class of Calabi-Yau threefolds, which are elliptic brations over a two-dimensional toric base. A holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base. T -duality on the bre implies that the topological string free energy also captures the BPSinvariants of D4-branes wrapping the elliptic bre and a class in the base. We verify this proposal by explicit computation of the BPS invariants of 3D4-branes on the rational elliptic surface.