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

The gauge-transformation superfield $\Lambda ={\Lambda }^a{T}_a$ is a dimensionless chiral superfield: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.