رشته‌های توپولوژیکی و منحنی‌های کوانتومی

Annotation 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. This title can be previewed in Google Books - http://books.google.com/books?vid=ISBN9789085550204 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