A scalar is never the highest component of a superfield, whether it appears in a superfield at all depends on the dimension of the spacetime.
12.
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.
13.
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.
14.
Every superfield, i . e . a field that depends on all coordinates of the superspace, may be expanded with respect to the new fermionic coordinates.
15.
For a superconformal field theory, the anomalous scaling dimension of a chiral superfield D = \ frac { 3 } { 2 } R where R is the R-charge.
16.
A superfield is a function defined in superspace which properly packages the various fields of a supermultiplet, namely, the array of fermion and boson fields related among themselves by supersymmetry.
17.
W _ \ alpha W _ \ beta is also a chiral superfield and we see that what acquires a nonzero VEV is not the F-term of this chiral superfield.
18.
W _ \ alpha W _ \ beta is also a chiral superfield and we see that what acquires a nonzero VEV is not the F-term of this chiral superfield.
19.
One may then define derivatives in the Grassmann directions, which take the first order term in the expansion of a superfield to the zeroeth order term and annihilate the zeroeth order term.
20.
The fact that the covariant derivatives anticommute with the supercharges means the supersymmetry transformation of a covariant derivative of a superfield is equal to the covariant derivative of the same supersymmetry transformation of the same superfield.
