Exakte Methoden in Eich- und String-Theorien

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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.