Open Access
August 2011 Sums over topological sectors and quantization of Fayet–Iliopoulos parameters
Simeon Hellerman, Eric Sharpe
Adv. Theor. Math. Phys. 15(4): 1141-1199 (August 2011).


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 the results of Bagger–Witten and more recent authors on quantization issues in supergravities from smooth moduli spaces to smooth moduli stacks, focusing particular attention on stacks that have gerbe structures.


Download Citation

Simeon Hellerman. Eric Sharpe. "Sums over topological sectors and quantization of Fayet–Iliopoulos parameters." Adv. Theor. Math. Phys. 15 (4) 1141 - 1199, August 2011.


Published: August 2011
First available in Project Euclid: 11 June 2012

zbMATH: 1250.83057
MathSciNet: MR2929685

Rights: Copyright © 2011 International Press of Boston

Vol.15 • No. 4 • August 2011
Back to Top