F-term
In theoretical physics, particularly in supersymmetric theories, an F-term is a term in the superpotential that, when non-zero, contributes to the potential energy of the theory and breaks supersymmetry. It arises from the auxiliary fields (F-fields) associated with chiral superfields.
More specifically, a chiral superfield contains a complex scalar field, a Weyl fermion, and an auxiliary field. The superpotential, W, is a holomorphic function of the chiral superfields. To find the vacuum energy of the theory, one minimizes the scalar potential. The F-term potential is given by a sum of terms, each of which is the square of the derivative of the superpotential with respect to a chiral superfield, as well as the complex conjugate of that derivative.
Mathematically, the F-term potential associated with a chiral superfield Φi is given by:
VF = Σi |∂W/∂Φi|2
where the sum is over all chiral superfields in the theory.
Supersymmetry is unbroken if and only if all F-terms vanish. In other words, supersymmetry is preserved in the vacuum only when ∂W/∂Φi = 0 for all i. If any of the F-terms are non-zero, the scalar potential is minimized when the F-fields take on non-zero values, leading to a non-zero vacuum energy. This indicates that supersymmetry is broken. The value of the F-term provides a measure of the scale of supersymmetry breaking.
F-term supersymmetry breaking is one of the main mechanisms for spontaneous supersymmetry breaking in supersymmetric models. The study of F-terms is important in model building because it helps to determine the properties of the vacuum state and the spectrum of particles in the theory. The structure of the superpotential and the resulting F-terms strongly influence the phenomenology of supersymmetric models.