Topological Strings and Quantum Curves

Details Topological Strings and Quantum Curves Topological Strings and Quantum Curves

2009-11-17

arxiv.org/abs/0911.3413v1

Physics

High Energy Physics

High Energy Physics - Theory

PhD thesis, July 2009, 308 pages, 65 figures

Scientific paper

This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for fermions on Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded into string theory. Secondly, this model is generalized to a web of dualities connecting topological string theory and N=2 supersymmetric gauge theories to a configuration of D-branes that intersect over a Riemann surface. This description yields a new perspective on topological string theory in terms of a KP integrable system based on a quantum curve. Thirdly, this thesis describes a geometric analysis of wall-crossing in N=4 string theory. And lastly, it offers a novel approach to construct metastable vacua in type IIB string theory.

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