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What is known about the classification of N=4 SCFTs with central charge 6?

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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.

This post has been migrated from (A51.SE)
asked Sep 14, 2011 in Theoretical Physics by Scott Carnahan (165 points) [ no revision ]

1 Answer

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For a survey on what was known in 1999 on the subject, there is the review A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6 by Werner Nahm and Katrin Wendland. I have not been following this subject, so I am not sure whether the current picture is substantially different.

Added

Some of the papers citing that review might also be relevant.

This post has been migrated from (A51.SE)
answered Sep 14, 2011 by José Figueroa-O'Farrill (2,125 points) [ no revision ]
Thank you. The Nahm-Wendland paper suggests that the moduli space of such theories is somewhat more subtle than I had been led to believe.

This post has been migrated from (A51.SE)

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