Quantization of Fayet-Iliopoulos Parameters in Supergravity

TL;DR

This paper explores the quantization of Fayet-Iliopoulos parameters in supergravity, linking it to geometric invariant theory and line bundle lifts, providing a geometric interpretation of the quantization condition.

Contribution

It introduces a geometric perspective on the quantization of Fayet-Iliopoulos parameters in supergravity using line bundles and GIT, connecting physics with algebraic geometry.

Findings

Fayet-Iliopoulos parameters are quantized in supergravity.

Quantization corresponds to line bundle lifts of group actions.

Connection established between supergravity parameters and GIT linearizations.

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.