D-term scalar potential ($V_D$)

Eliminating the real auxiliary field $D$ gives a nonnegative D-term scalar potential. For a $U(1)$ theory with charges $q_i$ and a Fayet–Iliopoulos parameter $\xi$, one convention gives $V_D=\frac{1}{2}[g{\sum }_i{q}_i|{\varphi }_i{|}^2+\xi {]}^2$.

A Fayet–Iliopoulos term is a gauge-invariant term linear in the auxiliary $D$ field of an Abelian vector multiplet. Supersymmetry is broken only if no charged-scalar configuration can make the shifted D-term vanish simultaneously with every F-term.