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 C 2 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 = 24k cannot exist for k 42. © SISSA 2007.