I am considering a particular limit of nonabelian YM theory. My resulting Lagrangian looks like $$\mathscr{L} = -\frac{1}{4}\bigg(\kappa^{i\,a}F^a_{ti} + F_{ij}^a F^{ij \, a}\bigg).$$ The field strength is given by $F^a_{\mu\nu} = \partial_\mu A^a_\nu - \partial_\nu A^a_\mu + gf^{abc}A^b_\mu A_\nu^c$ and $k^{a}_i$ is just a field (but it arises as a Lagrange multiplier). To find the symmetries, I define the most general infinitesimal transformations $$\begin{align} \delta A_t &= \xi^t \partial_t A_t + \xi^j \partial_j A_t + \alpha A_t + \beta^j A_j + \gamma^k \kappa_k \\ \delta A_i &= \xi^t \partial_t A_i + \xi^j \partial_j A_i + \delta_i A_t + \epsilon_i{}^j A_j + \zeta_i{}^k \kappa_k \\ \delta \kappa_i &= \xi^t \partial_t \kappa_i + \xi^j \partial_j \kappa_i + \eta_i A_t + \theta_i{}^j A_j + \iota_i{}^k \kappa_k. \end{align}$$ Here $\xi^\mu = \delta x^\mu$ and all the other parameters can depend on the spacetime coordinates.
However, with this method I fail to capture some symmetries. For example, this theory should be invariant under special conformal transformations, but it isn't. Is this method valid? Are there any subtleties when working with Lagrange multipliers in field theory?
