Sums over topological sectors and quantization of Fayet-Iliopoulos parameters

Details Sums over topological sectors and quantization of Fayet-Iliopoulos parameters Sums over topological sectors and quantization of Fayet-Iliopoulos parameters

2010-12-29

arxiv.org/abs/1012.5999v2

Physics

High Energy Physics

High Energy Physics - Theory

52 pages, LaTeX; v2: typo fixed

Scientific paper

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.

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