Curiosities above c = 24

Abstract

Two-dimensional rational CFT are characterised by an integer $\ell$, related to the number of zeroes of the Wronskian of the characters. For two-character RCFT's with $\ell <6$ there is a finite number of theories and most of these are classified. Recently it has been shown that for $\ell \ge 6$ there are infinitely many admissible characters that could potentially describe CFT's. In this note we examine the $\ell =6$ case, whose central charges lie between 24 and 32, and propose a classification method based on cosets of meromorphic CFT's. We illustrate the method using theories on Kervaire lattices with complete root systems. In the process we construct the first known two-character RCFT's beyond $\ell =2$.

arXiv comment20 pages, v4: Corrected some entries in Tables A.1 to A.5 in Appendix A

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• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
• Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
• Discreteness and Integrality in Conformal Field Theory
• Wronskian Indices and Rational Conformal Field Theories
• Fake Z
• Meromorphic Cosets and the Classification of Three-Character CFT
• Universal Correlators and Novel Cosets in 2d RCFT
• New meromorphic CFTs from cosets
• Two approaches to the holomorphic modular bootstrap
• Modular linear differential equations for four-point sphere conformal blocks
• Rényi entropy of single-character CFTs on the torus