In theoretical physics, the Fayet–Iliopoulos D-term (introduced by Pierre Fayet and John Iliopoulos) is a D-term in a supersymmetric theory obtained from a vector superfield V simply by an integral over all of superspace:

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

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

• Fayet, P.; Iliopoulos, J. (1974). "Spontaneously broken supergauge symmetries and goldstone spinors". Physics Letters B. Elsevier BV. 51 (5): 461–464. doi:10.1016/0370-2693(74)90310-4. ISSN 0370-2693.