Sums over topological sectors and\n\t\t\t\tquantization of Fayet–Iliopoulos\n\t\t\t\tparameters

Abstract

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