Quantization of Fayet-Iliopoulos parameters in supergravity

In this talk we will discuss Fayet-Iliopoulos parameters in four dimensional N=1 supergravity. Although for many years there was lore that they did not exist in supergravity, it was recently argued by Seiberg that they could exist but are quantized, and we will review that quantization. We will also discuss related issues in nonlinear sigma models with a restriction on nonperturbative sectors. In such theories, the FI quantization above is modified, and we will discuss how that modification has a simple mathematical understanding.