弦论的相关研究

String theory has been an active area of research for several decades. My own research focus on several aspects, including topological string theory, Calabi-Yau manifolds, AdS/CFT correspondence, and string cosmology. Recently there have been some interests in refined topological string theory on Calabi-Yau manifold. These research is inspired by the Nekrasov partition function for Seiberg-Witten gauge theory, which has two deformation parameters and is known as Omega deformation. The higher order terms of the Nekrasov function expanded around small parameters are similar to the higher genus amplitudes in topological string theory on Calabi-Yau manifolds, and can be studied by the method of holomorphic anomaly equations. One can fix the holomorphic ambiguity using the gap boundary conditions. The conventional unrefined topological string theory corresponds to the case of vanishing sum of the two parameters. In our previous works, the holomorphic anomaly equations and the gap boundary conditions are generalized to the refined case of arbitrary Omega deformations, in order to solve the corresponding higher order amplitudes in the Nekrasov function. It is interesting to apply the techniques to refined topological string theory on Calabi-Yau manifolds.

弦论和相关的方向是目前国际学术界的一个热门研究方向。这个领域发展日新月异，各种新的结果层出不穷。我主要从事下面几个方面的研究。首先可以把我们提出的计算拓扑弦论的技术应用到更多的Calabi-Yau空间上。继续推广在超对称规范理论上的应用，可其他超对称规范理论的方法，特别是矩阵模型方法联系起来。在这个过程中，我们希望发现新的拓扑弦论的技术，推进这个领域的发展。另外，我还继续 AdS/CFT对应性，弦宇宙学等方面的研究。

拓扑弦论是弦论的一个重要分支，主要研究弦论中的一些拓扑自由度，特别是卡拉比－丘流形的拓扑性质。本项目期间，取得拓扑弦理论的一系列进展，包括全纯反常方程，模反常方程的推导，精细拓扑弦理论和矩阵模型的关系，运用全纯反常方程和数学上的Weak Jacobi Forms 理论来计算精细拓扑弦配分函数。