An overview of Bagger-Witten line bundles

We give a brief overview of recent progress in understanding Bagger-Witten line bundles, which are bundles over moduli spaces of two-dimensional N=2 SCFTs whose existence is a consequence of the global U(1)_R symmetry of the theories. Our overview includes a discussion of applications in supergravities coupled to gauge theories, a proposal for a purely geometric interpretation, and explicit examples over moduli spaces of Calabi-Yau manifolds. (Contribution to the proceedings of the workshop "The geometry of moduli spaces in string theory" (Matrix institute, Australia, September 2024).)