In theoretical physics, one often analyzes theories with supersymmetry in which D-terms play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using a superspace. This superspace involves four extra fermionic coordinates \( \theta ^{1},\theta ^{2},{\bar {\theta }}^{1},{\bar {\theta }}^{2} \), transforming as a two-component spinor and its conjugate.
Every superfield, i.e. a field that depends on all coordinates of the superspace, may be expanded with respect to the new fermionic coordinates. The generic kind of superfields, typically a vector superfield, indeed depend on all these coordinates. The last term in the corresponding expansion, namely \( D \theta^1\theta^2\bar\theta^1\bar\theta^2 \), is called the D-term.
Manifestly supersymmetric Lagrangians may also be written as integrals over the whole superspace. Some special terms, such as the superpotential, may be written as integrals over \( \theta \)s only, which are known as F-terms, and should be contrasted with the present D-terms.
See also
F-term
Supersymmetric gauge theory
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