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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

P. Fayet, J. Iliopoulos, Spontaneously Broken Supergauge Symmetries And Goldstone Spinors., Phys.Lett.B51:461-464,1974. (Entry in SPIRES)

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