D-term explained

In theoretical physics, the D-term is the final term in the expansion of a vector superfield over fermionic coordinates. A superfield is a field that depends on all coordinates of the superspace, which is the coordinate space of a theory exhibiting supersymmetry.

A superspace can be expressed as a combination of ordinary space dimensions (x, y, z, ...,) and fermionic dimensions. 4D N = 1 global supersymmetry may be written using a superspace involving 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 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. A D-term obtained from a vector superfield solely by an integral over all of superspace is known as a Fayet–Iliopoulos D-term.^[1] 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

Notes and References

1. Dvali, Gia . Kallosh, Renata . Van Proeyen, Antoine . 2004 . D-term strings . Journal of High Energy Physics . 2004 . 1 . 10.1088/1126-6708/2004/01/035.