Coursera Spring Sale
40% Off Coursera Plus Annual!
Grab it
Explore the intricate relationship between symmetries and moduli spaces in string compactifications through this differential geometry and physics seminar lecture. Begin with the well-established Calabi-Yau framework, examining the classical benchmark of line bundles over Calabi-Yau complex structure moduli spaces and their physical interpretation as Berry phases of spectral flow operators in worldsheet superconformal field theory. Investigate how this foundational understanding evolves when moving beyond the familiar Calabi-Yau setting, specifically examining c=1 theories with worldsheet anomalies and G_2 and Spin(7) compactifications where U(1)_R symmetry is absent. Discover how anomalies and non-invertible symmetries emerge in these more general contexts, and consider the open questions surrounding potential mathematical structures that might exist over moduli spaces in these extended frameworks. Gain insight into cutting-edge research that bridges differential geometry and theoretical physics, focusing on the fundamental question of what new geometric and topological structures might govern string compactifications beyond the well-understood Calabi-Yau case.
