Monster Anatomy

Abstract

We investigate the two-dimensional conformal field theories (CFTs) of $c=\frac{47}{2}$, $c=\frac{116}{5}$ and $c=23$ `dual' to the critical Ising model, the three state Potts model and the tensor product of two Ising models, respectively. We argue that these CFTs exhibit moonshines for the double covering of the baby Monster group, $2\cdot \mathbb{B}$, the triple covering of the largest Fischer group, $3\cdot {\text{Fi}}_{24}^{\prime }$ and multiple-covering of the second largest Conway group, $2\cdot 2^{1+22}\cdot {\text{Co}}_2$. Various twined characters are shown to satisfy generalized bilinear relations involving Mckay-Thompson series. We also rediscover that the `self-dual' two-dimensional bosonic conformal field theory of $c=12$ has the Conway group ${\text{Co}}_0\simeq 2\cdot {\text{Co}}_1$ as an automorphism group.

arXiv comment23 pages, revised according to suggestions from JHEP referee

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• Mathieu twining characters for K3
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Cited by in corpus (7)

• Conformal Field Theories with Sporadic Group Symmetry
• Bootstrapping Fermionic Rational CFTs with Three Characters
• Relative Anomaly in (1+1)d Rational Conformal Field Theory
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• Meromorphic Cosets and the Classification of Three-Character CFT
• Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations
• Duality Defect of the Monster CFT