Degeneration, Geometry and Duality in String Theory

Explore the intricacies of dualities in compactified string theories and their extension across moduli space in this comprehensive lecture. Delve into the concept of generalized T-duality, examining its role in the Strominger-Yau-Zaslow interpretation of mirror symmetry. Investigate the duality between type I' string theory compactified on a 3-torus and type IIA string theory on an orbifold limit of K3, and its extrapolation to a generalized duality with IIA on a degenerate limit of K3. Analyze the transformation of D8-branes to Kaluza-Klein monopoles and orientifold planes to Tian-Yau spaces. Examine the approximate metric that enables an explicit SYZ duality, providing a geometric dual of exotic strong-coupling phenomena and additional T-fold duals. Gain insights into advanced concepts in string theory and their geometric interpretations through this in-depth exploration of degeneration, geometry, and duality.