D-term

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 θ 1 , θ 2 , θ ¯ 1 , θ ¯ 2 {displaystyle heta ^{1}, heta ^{2},{ar { heta }}^{1},{ar { heta }}^{2}} , transforming as a two-component spinor and its conjugate. 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 θ 1 , θ 2 , θ ¯ 1 , θ ¯ 2 {displaystyle heta ^{1}, heta ^{2},{ar { heta }}^{1},{ar { heta }}^{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 θ 1 θ 2 θ ¯ 1 θ ¯ 2 {displaystyle D heta ^{1} heta ^{2}{ar { heta }}^{1}{ar { heta }}^{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 θ {displaystyle heta } s only, which are known as F-terms, and should be contrasted with the present D-terms.