论文标题
诺比尔镜子和格罗莫夫的不变式
Nonabelian mirrors and Gromov-Witten invariants
论文作者
论文摘要
在本文中，我们提出了有关非亚伯镜子时期的Picard-fuchs方程。我们的PICARD-FUCHS方程中的参数数量是Nonabelian GLSM的量规组的等级，最终将其减少到Kähler参数的实际数量。这些Picard-fuchs方程是简洁而新颖的。我们通过重现现有的数学结果，即硕士和卡拉比流形的歧管，以作为司芒氏菌的完整交集来证明我们的建议是合理的。此外，我们的方法可以应用于其他非亚伯GLSM，因此我们计算了其他一些Fano空间的Picard-fuchs方程，这些方程在文献中没有计算出来。最后，可以从我们的picard-fuchs方程中读取镜子的同时值的生成功能。 Using these generating functions, we compute Gromov-Witten invariants of various Calabi-Yau manifolds, including complete intersection Calabi-Yau manifolds in Grassmannians and non-complete intersection Calabi-Yau examples such as Pfaffian Calabi-Yau threefold and Gulliksen-Negård Calabi-Yau threefold, and find agreement with existing results in the literature.我们为不完整的交点Calabi-yau歧管提出的生成功能确实是新的。
We propose Picard-Fuchs equations for periods of nonabelian mirrors in this paper. The number of parameters in our Picard-Fuchs equations is the rank of the gauge group of the nonabelian GLSM, which is eventually reduced to the actual number of Kähler parameters. These Picard-Fuchs equations are concise and novel. We justify our proposal by reproducing existing mathematical results, namely Picard-Fuchs equations of Grassmannians and Calabi-Yau manifolds as complete intersections in Grassmannians. Furthermore, our approach can be applied to other nonabelian GLSMs, so we compute Picard-Fuchs equations of some other Fano-spaces, which were not calculated in the literature before. Finally, the cohomology-valued generating functions of mirrors can be read off from our Picard-Fuchs equations. Using these generating functions, we compute Gromov-Witten invariants of various Calabi-Yau manifolds, including complete intersection Calabi-Yau manifolds in Grassmannians and non-complete intersection Calabi-Yau examples such as Pfaffian Calabi-Yau threefold and Gulliksen-Negård Calabi-Yau threefold, and find agreement with existing results in the literature. The generating functions we propose for non-complete intersection Calabi-Yau manifolds are genuinely new.
