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Intheoretical physics, one often analyzes theories withsupersymmetry in whichF-terms play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using asuperspace. This superspace involves four extra fermionic coordinates${\displaystyle {\theta }^1,{\theta }^2,{\overline{\theta }}^1,{\overline{\theta }}^2}$, transforming as a two-componentspinor 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-calledchiral superfields, that only depend on the variables${\displaystyle \theta }$ but not their conjugates. The last term in the corresponding expansion, namely${\displaystyle F{\theta }^1{\theta }^2}$, is called theF-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${\displaystyle \int d^{4}xF(x)}$ is invariant under SUSY transformations as long as boundary terms vanish. Thus F-terms may be used in constructing supersymmetric actions.

Manifestly-supersymmetricLagrangians may also be written asintegrals over the whole superspace. Some special terms, such as thesuperpotential, may be written as integrals over${\displaystyle \theta }$s 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.

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