On the Conifold Point in Topological String Theory
Lei You · 2025
This thesis reviews the role of the conifold point in topological string theory, focusing on its significance in enumerative geometry of Calabi-Yau threefolds. We provide an overview of the topological A-string and B-string, covering some basic mathematical structures such as cohomological field theories and Gromov-Witten invariants. The conifold singularity is explored in geometric transitions, with emphasis on the large N duality linking Chern-Simons theory on S3 to the resolved conifold. A central topic is the conifold gap conjecture, which predicts a universal gap structure in the higher-genus B-model amplitudes near the conifold point. This structure provides critical conditions to determine higher-genus Gromov-Witten invariants of Calabi-Yau threefolds. We also survey some gap structures in other situations.