Differential Geometry and Physics Seminar

Speaker: Xingyang Yu, Virginia Tech

Title: Symmetries and Moduli Spaces: Baby Steps beyond Calabi-Yau

Abstract: I will explore the interplay between symmetries and moduli spaces in string compactifications, starting from the familiar Calabi–Yau case and then taking some baby steps toward more general settings. A classical benchmark is the line bundle over Calabi–Yau complex structure moduli space, whose physical counterpart corresponds to the Berry phase of the spectral flow operator in worldsheet SCFT. I will review this story and then discuss how it begins to change in c=1 theories with worldsheet anomalies, and in G_2 and Spin(7) compactifications where U(1)_R symmetry is absent. The goal is not a finished framework, but to highlight how anomalies and non-invertible symmetries may enter the picture and to raise open questions about what kinds of structures might live over moduli spaces beyond Calabi–Yau.