Constraints on extremal self-dual CFTs

Abstract

We argue that the existence of a modular differential equation implies that a certain vector vanishes in Zhu's C2 quotient space, and we check this assertion in numerous examples. If this connection is true in general, it would imply that the recently conjectured extremal self-dual conformal field theories at c=24 k cannot exist for k\geq 42.

16 pages LaTeX; v1: rewritten to make paper more self-contained, modified conjecture slightly (this has no effect on main conclusion), added references

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