Quantization of Fayet-Iliopoulos Parameters in Supergravity

Abstract

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.

21 pages, utarticle class; v2: typos and tex issue fixed

References in corpus (19)

• A New Cohomology Theory for Orbifold
• Cluster decomposition, T-duality, and gerby CFT's
• GLSM's for gerbes (and other toric stacks)
• Non-birational twisted derived equivalences in abelian GLSMs
• String compactifications on Calabi-Yau stacks
• Modifying the Sum Over Topological Sectors and Constraints on Supergravity
• Homological projective duality for Grassmannians of lines
• Discrete Torsion
• Notes on gauging noneffective group actions
• Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group
• SU(4) Instantons on Calabi-Yau Threefolds with Z_2 x Z_2 Fundamental Group
• Sheaves on Toric Varieties for Physics
• D-branes, orbifolds, and Ext groups
• On Gromov-Witten theory of root gerbes
• On the geometry of quiver gauge theories (Stacking exceptional collections)
• Duality theorems for étale gerbes on orbifolds
• Notes on discrete torsion in orientifolds
• On degree zero elliptic orbifold Gromov-Witten invariants
• On the C^n/Z_m fractional branes

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• On Fayet-Iliopoulos terms and de Sitter vacua in supergravity: some easy pieces
• Fluxbranes: Moduli Stabilisation and Inflation
• Inflation with Fayet-Iliopoulos Terms
• Superconformal D-Term Inflation
• Bubbles of Nothing and Supersymmetric Compactifications
• General aspects of heterotic string compactifications on stacks and gerbes
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Topological mass generation in gapless systems
• A few recent developments in 2d (2,2) and (0,2) theories
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• Supermassive Cosmic String Compactifications
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$
• Unstable Nambu-Goldstone modes
• Bagger-Witten line bundles on moduli spaces of elliptic curves
• Neutralizing Topological Obstructions to Bubbles of Nothing
• A QCD R-Axion
• Global aspects of moduli spaces of 2d SCFTs
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory
• Rediscovery of Cooper pair factor