Exakte Methoden in Eich- und String-Theorien

该项目的目标是回答关于弦和超对称规范理论的非微扰性质的基本问题。例如，（拓扑）弦的渐近亏格展开中的项一般地随着（2g）！局部场论中的g！鉴于不同的渐近性，Kodaira-Spencer作用量如何作为拓扑弦的场论作用量？哪些非微扰效应决定了渐近展开式中的次主导贡献？对称性是非微扰破缺的吗？为了得到描述物理量（如黑洞的熵）的收敛级数，必须加上哪些膜态？这样的非微扰完备化是背景独立的吗？在拓扑领域回答这些问题的期望是基于新开发的方法来解决这些理论，通过镜像对称，矩阵模型和陈-西蒙斯理论的大N-扩展，对偶性，模块性，全纯性和可积性。这些技术的发展也将导致改善预测的低能量有效的行动中使用的字符串模型的建设。该研究领域与代数和辛几何，组合学和自守形式理论有积极的重叠。

The goal of the project is to answer fundamental questions concerning the non-perturbative properties of string- and super symmetric gauge theories. For example the terms in the asymptotic genus expansion of the (topological) string grow generically with (2g)!, the ones of local field theory with g!. In view of the different asymptotics how can the Kodaira-Spencer action serve as field theory action for the topological string? Which non-perturbative effects determine the sub-leading contributions in the asymptotic expansion? Are symmetries non-perturbatively broken? Which brane states have to be added to obtain convergent series describing physical quantities, e.g. the entropy of black holes? Are such non-perturbative completions background independent? The expectation to answer these questions in the topological sectors is based on newly developed methods to solve these theories via mirror symmetry, large N-expansion of matrix models and Chern-Simons theories, duality, modularity, holomorphicity and integrability. The development of these techniques will also lead to improved predictions for the low energy effective actions used in string model building. The research area has active overlap with algebraic and symplectic geometry, combinatorics and the theory of automorphic forms.