These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A topological field theory can be constructed whose observables are only the elements of the chiral ring. When coupled to gravity, this leads to topological string theory. The identification of the topological string A- and B-models by mirror symmetry leads to surprising connections in mathematics and provides tools for exact computations as well as new insights in physics. A recursive construction of the higher genus amplitudes of topological string theory expressed as polynomials is reviewed.
翻译:这些是清华大学数学中心一系列关于镜像对称和地形弦理论的讲座的笔记。 N=2 超正正代数、其变形和手环都经过了审查。可以构建一个其可观测只是手环元素的地形理论。当与重力相结合时,这会导致地形弦理论。通过镜像对称确定表象弦A和B模型,在数学方面导致令人吃惊的联系,提供了精确计算的工具以及物理学方面的新洞察力。对以多面形体表示的较高地形弦理论精度的循环构造进行了审查。