In supersymmetric theories of fields in fundamental representation we write the Kahler interactions as

\begin{equation}

\Phi ^\dagger e ^{ 2 qV } \Phi

\end{equation}

where $V$ is the vector superfield in the fundamental representation. This is necessary to keep the fields which transform as,

\begin{align}

& \Phi \rightarrow e ^{ i \Lambda } \Phi , \quad V \rightarrow V - \frac{ i }{ 2} \left( \Lambda - \Lambda ^\dagger \right)

\end{align}

gauge invariant.

I would naively think that this requirement would transfer over to fields in other representations. However recently I reading a paper where they introduce fields in the adjoint representation, $\Phi _a$, and I believe they didn't include the gauge contribution and just wrote,

\begin{equation}

\Phi _a ^\dagger \Phi _a

\end{equation}

(though they don't state or write this explicitly so I'm not sure). This doesn't make sense to me since adjoint representation fields still transform. Is there a reason why this would be justified, or did I misunderstand the paper?