F-term

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This article is about F-term in theoretical physics. For the patent classification used in Japan, see F-term (patent law).

In theoretical physics, one often analyzes theories with supersymmetry in which F-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 , 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. There exists a special kind of superfields, the so-called chiral superfields, that only depend on the variables θ but not their conjugates. The last term in the corresponding expansion, namely Fθ¹θ², is called the F-term. Applying an infinitesimal supersymmetry transformation to a chiral superfield results in yet another chiral superfield whose F-term, in particular, changes by a total derivative. This is significant because then : is invariant under SUSY transformations as long as boundary terms vanish. Thus F-terms may be used in constructing supersymmetric actions.

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.