I was talking about K3 surfaces with some physicists, and one of them told me that the N=4 superconformal field theories with central charge 6 are expected to be relatively scarce. In particular, one should expect a lot of a priori different theories (e.g., those coming from sigma models whose targets are different hyperkähler surfaces, or the Gepner model) to be isomorphic. I have not found similar statements in the mathematical literature, but it sounds like a statement that, if suitably tweaked, could conceivably make sense to mathematicians.
Question: Where can I find such a claim (and perhaps additional justification)?
Also, I am curious to know if there are underlying physical principles behind such a claim, or if it was conjectured due to a scarcity of characters (i.e., the space of suitable modular/Jacobi forms is small), or perhaps some combination.