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that appears in D-flatness conditions (and whose square enters the ordinary potential) is additively shifted by
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Because a natural trace must be a part of the expression, the action only exists for U(1) vector superfields.
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Fayet, P.; Iliopoulos, J. (1974). "Spontaneously broken supergauge symmetries and goldstone spinors".
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In terms of the components, it is proportional simply to the last auxiliary D-term of the superfield
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204:{\displaystyle S_{FI}=\xi \int d^{4}\theta \,V}
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238:{\displaystyle \xi }
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