= Pure-scalar truncation of a superfield
A function $S(x,\theta,\bar\theta)=\phi(x)$ is an allowed special configuration of an unconstrained <superfield>. The subspace where all other components remain zero is not invariant: $\delta S=(i\theta\sigma^\mu\bar\epsilon-i\epsilon\sigma^\mu\bar\theta)\partial_\mu\phi$ produces components depending on <Grassmann variables> whenever $\phi$ is nonconstant. Thus an isolated spacetime <scalar field> is not closed under <supersymmetry>. A constant gauge-singlet value is a trivial invariant exception.
Back to article page
