Fayet–Iliopoulos D-term

${\displaystyle S_{FI}=\xi \int d^{4}\theta \,V}$

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 ${\displaystyle \xi }$, the coefficient.

References