Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections
Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections
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拓扑弦振幅、完全交集 Calabi-Yau 空间和阈值校正
DOI：
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发表时间：
2004
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通讯作者：
E. Scheidegger
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文献类型：
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作者：
A. Klemm;Maximilian Kreuzer;Erwin Riegler;E. Scheidegger
给出了复曲面环境簇中Calabi-Yau完全相交的镜像对的最完整的列表，并给出了在这些紧致Calabi-Yau空间上求解拓扑弦和计算更高亏格振幅的方法.这些辛不变量用于消除示例中的冗余。B模型传播子的构造导致相容性条件，该条件约束多参数镜像映射。对于K3纤维化的Calabi-Yau空间，没有可约纤维，我们找到了封闭的公式，所有亏格的纤维方向的纤维化的几何贡献。如果这种几何的杂合对偶是已知的，则可以用有助于引力阈值校正的BPS态的简并度来确定更高的属不变量，并且完成了微扰机制中弦对偶的所有属检查。然而，我们发现，BPS简并不唯一固定的杂合弦的非微扰完成。对于这些几何形状，我们可以用唐纳森-托马斯不变量来写拓扑配分函数，并对拓扑弦中的S-对偶进行非平凡检查。我们进一步研究通过崩溃的D5德尔佩佐表面和发生的免费2个杂种优势，导致一类新的杂种优势的转换。
We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free 2 quotients that lead to a new class of heterotic duals.