It turns out that, in systems exhibiting the quantum Hall effect, chiral excitations belonging to different edge channels have different propagation speeds, as people, including myself, have discussed in numerous papers. There really usually is a non-trivial "spectrum" of different propagation speeds. This implies that a theory describing such a system is NOT conformal in the strict sense of the word!
A conformal transformation is something like an analytic generalization of a Lorenz transformation, in which c is constant.
In other sources it is an angle preserving transformation , like f(z)
Perhaps this idea comes the Laughlin early handling of the problem in terms of the Complex?
However I agree such term is not the best for QHE.
The problem is that many incompressible Hall fluids have several different "c's", depending on which chiral edge channel you consider; i.e., the propagation speeds of different chiral edge modes are usually different from each other!
(Quite apart from that, there tends to be a small amount of dispersion in the propagation of edge modes - but you may want to neglect that.)