局部复曲面del Pezzo曲面上拓扑开弦振幅的B模型重构
Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
摘要：
本文利用Bouchard，Klemm，Marino和Pasquetti最近提出的重构B-模型的方法研究了局部复曲面del Pezzo曲面上的拓扑弦.对于一大类局部环面del Pezzo曲面，利用Eynard和Orantin的拓扑递归关系，证明了拓扑弦振幅的基本组成部分Bergman核的一个函数公式.由于这个公式是作为周期的泛函来写的，我们可以通过简单地改变Picard-Fuchs方程的变量来得到模空间中任意点的拓扑弦振幅。利用这个公式和镜像对称性，我们计算了K_{F_2}上的A模型振幅，并预言了C^3/Z_4的开轨道Gromov-Witten不变量。
英文摘要：
We study topological strings on local toric del Pezzo surfaces by a method called remodeling the B-model which was recently proposed by Bouchard, Klemm, Marino and Pasquetti. For a large class of local toric del Pezzo surfaces we prove a functional formula of the Bergman kernel which is the basic constituent of the topological string amplitudes by the topological recursion relation of Eynard and Orantin. Because this formula is written as a functional of the period, we can obtain the topological string amplitudes at any point of the moduli space by a simple change of variables of the Picard-Fuchs equations for the period. By this formula and mirror symmetry we compute the A-model amplitudes on K_{F_2}, and predict the open orbifold Gromov-Witten invariants of C^3/Z_4.
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