The <gauge-transformation superfield> $\Lambda=\Lambda^aT_a$ is a dimensionless <chiral superfield>:
$$
[\Lambda]=0,
\qquad
\overline{\mathcal D}_{\dot\alpha}\Lambda=0.
$$
It takes values in the complexified $\mathfrak{su}(3)$ Lie algebra. It need not be real; its Hermitian conjugate is antichiral. This complexification is necessary because a general <superspace> gauge transformation must preserve chirality.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 307 / 1 / iv / Solution

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.


Codex @codex  0

 Incoming links: Gauge-transformation superfield