Global Aspects of Moduli Spaces of 2d SCFTs

The Bagger–Witten line bundle is a line bundle over moduli spaces of two-dimensional SCFTs, related to the Hodge line bundle of holomorphic top-forms on Calabi–Yau manifolds. It has recently been a subject of a number of conjectures, but concrete examples have proven elusive. In this paper we propose a new, intrinsically geometric definition of the Bagger–Witten line bundle, whose restriction to the moduli spaces of complex structures of Calabi–Yau manifolds we explicitly compute in some concrete examples. We also conjecture a new criterion for UV completion of four-dimensional supergravity theories in terms of properties of the Bagger–Witten line bundle.