Gauge-transformation superfield

In four-dimensional $\mathcal{N}=1$ supersymmetry, a gauge-transformation superfield is a dimensionless chiral, Lie-algebra-valued parameter $\Lambda$. Its complex nature allows gauge transformations to preserve chirality.

A supergauge transformation acts on a charged chiral superfield and vector superfield together. In one common convention, ${\Phi }^{\prime }=e^{-2i\Lambda }\Phi$ and $e^{2V^{\prime }}=e^{-2i{\Lambda }^{†}}{e}^{2V}{e}^{2i\Lambda }$.