Fayet–Iliopoulos D-term explained

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:

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

\xi , the coefficient.

References

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