Quantization of Fayet-Iliopoulos Parameters in Supergravity

Details Quantization of Fayet-Iliopoulos Parameters in Supergravity Quantization of Fayet-Iliopoulos Parameters in Supergravity

2010-08-02

arxiv.org/abs/1008.0419v2

Phys.Rev.D83:085010,2011

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.83.085010

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.

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