# Global aspects of moduli spaces of 2d SCFTs

## TL;DR

This paper investigates the Bagger-Witten line bundle over moduli spaces of 2D SCFTs, proposing a geometric definition, providing examples, and conjecturing a criterion for UV completion of 4D supergravity theories.

## Contribution

It offers a new geometric perspective on the Bagger-Witten line bundle and introduces a conjecture linking its properties to supergravity UV completion.

## Key findings

- Proposed an intrinsic geometric definition of the Bagger-Witten line bundle.
- Provided concrete examples of the Bagger-Witten line bundle structure.
- Conjectured a new criterion for UV completion of 4D supergravity theories.

## Abstract

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 collect several results on this structure, including a proposal for an intrinsic geometric definition over moduli spaces of Calabi-Yau manifolds and some additional 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.