F-term

{{Short description|Term found in supersymmetric theories}}

{{about|F-term in theoretical physics|the patent classification used in Japan|F-term (patent law)}}

{{One source|date=April 2025}}

In theoretical physics, one often analyzes theories with supersymmetry in which F-terms{{cite journal |title=On F-term contribution to effective action |date=2007 |publisher=Cornell University |doi=10.1088/1126-6708/2007/08/052 |arxiv=hep-th/0611278 |last1=Shadchin |first1=Sergey |journal=Journal of High Energy Physics |issue=8 |page=052 |bibcode=2007JHEP...08..052S }} 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 $\backslash theta^1,\backslash theta^2,\backslash bar\backslash theta^1,\backslash bar\backslash theta^2$, 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. There exists a special kind of superfields, the so-called chiral superfields, that only depend on the variables $\backslash theta$ but not their conjugates. The last term in the corresponding expansion, namely $F\; \backslash theta^1\backslash theta^2$, 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 $\backslash int\{d^4x\backslash ,\; F(x)\}$ 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 $\backslash theta$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.