Constraints on extremal self-dual CFTs. (English) Zbl 1245.81239
Summary: 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 \(k \geq 42\).
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
Keywords:
self-dual CFTsReferences:
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