Sums over topological sectors and quantization of Fayet-Iliopoulos parameters

TL;DR

This paper explores the quantization of Fayet-Iliopoulos parameters in supergravity, emphasizing the role of gerbe structures in moduli spaces and their impact on topological defects and dualities.

Contribution

It extends quantization analysis to supergravity theories with gerbe-structured moduli stacks, connecting topological defects and dualities in these frameworks.

Findings

Gerbe structures influence FI parameter quantization.

Examples of gerby moduli spaces in string theory are discussed.

Global topological defects are linked to gerbe structures.

Abstract

In this paper we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories with altered nonperturbative sectors, which were recently used to argue a fractional quantization condition. Nonlinear sigma models with altered nonperturbative sectors are the same as nonlinear sigma models on special stacks known as gerbes. After reviewing the existing results on such theories in two dimensions, we discuss examples of gerby moduli `spaces' appearing in four-dimensional field theory and string compactifications, and the effect of various dualities. We discuss global topological defects arising when a field or string theory moduli space has a gerbe structure. We also outline how to generalize results of Bagger-Witten and more recent authors on quantization issues in supergravities from smooth manifolds to smooth moduli stacks, focusing particular attention on stacks that have gerbe structures.