Superfield

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In theoretical physics, one often analyzes theories with supersymmetry in which superfields play a very important role. In four dimensions, the simplest example - namely the minimal N=1 supersymmetry - may be written using a superspace. This superspace involves four extra fermionic coordinates , transforming as a two-component spinor and its conjugate.

A more coordinate-free description, at least for N=1 SUSY, of the superspace is that it's the quotient space of the superPoincaré group by the Lorentz group.

Every superfield, i.e. a field that depends on all coordinates of the superspace (or in other words, an element of a module of the algebra of functions over superspace), may be expanded with respect to the new fermionic coordinates. There exists a special kind of superfields, the so-called chiral superfields, that, in the chiral representation of supersymmetry, depend only on the variables θ but not their conjugates. The last term in the corresponding expansion, namely Fθ¹θ², is called the F-term. Other superfields include vector superfields.

There also exist superfields in theories with larger supersymmetry.

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 θs only. They are also referred to as F-terms, much like the terms in the ordinary potential that arise from these terms of the supersymmetric Lagrangian.