Consider the following abelian Chern-Simons theory in 2+1 dimensions:

\[\mathcal{L}_{CS} = \frac{\kappa}{2} \epsilon^{\mu\nu\rho} A_{\mu}\partial_{\nu}A_{\rho}\]

Are there unique Universality classes for each value of \(\kappa\), or all Lagrangian densities of the above form but with different non-zero \(\kappa\)values belong to the same universality class? In other words, is it justified to absorb \(\kappa\)by rescaling the gauge field variables? Obviously there is a good reason that people keep \(\kappa\) explicit, but I don't see the problem with such a seemingly innocuous rescaling. Does the rescaling meddle with the gauge transformation on the edge?