D-term

Intheoretical physics,one often analyzes theories withsupersymmetryin whichD-termsplay an important role. In four dimensions, the minimal N=1 supersymmetry may be written using asuperspace.This superspace involves four extra fermionic coordinates$\theta ^{1},\theta ^{2},{\bar {\theta }}^{1},{\bar {\theta }}^{2}$,transforming as a two-componentspinorand 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 avector 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 supersymmetricLagrangiansmay also be written asintegralsover the whole superspace. Some special terms, such as thesuperpotential,may be written as integrals over$\theta$s only, which are known asF-terms,and should be contrasted with the present D-terms.

See also

• F-term
• Supersymmetric gauge theory