Fayet-Iliopoulos D-term

In theoretical physics, the Fayet-Iliopoulos D-term is a D-term in a supersymmetric theory obtained from a vector superfield "V" simply by an integral over all of superspace:
* $S\_\{FI\}\; =\; xi\; int\; d^4\; heta\; ,\; V$Because a natural trace must be a part of the expression, the action only exists for U(1) vector superfields.

In terms of the components, it is proportional simply to the last auxiliary D-term of the superfield "V". It means that the corresponding "D" that appears in D-flatness conditions (and whose square enters the ordinary potential) is additively shifted by $xi$, the coefficient.