This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded in 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 constuct metastable vacua in type IIB string theory.
Author(s): Lotte Hollands
Series: Pallas Proefschriften
Publisher: Pallas Publications
Year: 2009
Language: English
Pages: 309
Contents......Page 8
Introduction......Page 10
Calabi-Yau Geometry......Page 24
I-brane Perspective on Vafa-Witten Theory and WZW Models......Page 40
Topological Strings, Free Fermions and Gauge Theory......Page 78
Quantum Integrable Hierarchies......Page 122
Quantum Curves in Matrix Models and Gauge Theory......Page 156
Dyons and Wall-Crossing......Page 198
Fluxes and Metastability......Page 244
Level-rank duality......Page 282
Bibliography......Page 286
Samenvatting......Page 302
Acknowledgments......Page 308
