Topological Strings and Quantum Curves

TL;DR

This thesis explores the deep connections between topological strings, quantum curves, and dualities in string theory, providing new insights into integrable systems, wall-crossing phenomena, and metastable vacua.

Contribution

It introduces a novel perspective on topological string theory via quantum curves and integrable systems, and links various dualities in string theory with geometric and physical insights.

Findings

Embedding of Vafa-Witten duality into string theory

Connection of topological strings to KP integrable systems

Analysis of wall-crossing and metastable vacua in string theory

Abstract

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.