Monster anatomy

<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title>
<jats:p>We investigate the two-dimensional conformal field theories (CFTs) of <jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$$ c=\frac{47}{2} $$</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>c</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mn>47</mml:mn>
<mml:mn>2</mml:mn>
</mml:mfrac>
</mml:math>
</jats:alternatives>
</jats:inline-formula>
<jats:sub>,</jats:sub>
<jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$$ c=\frac{116}{5} $$</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>c</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mn>116</mml:mn>
<mml:mn>5</mml:mn>
</mml:mfrac>
</mml:math>
</jats:alternatives>
</jats:inline-formula> and <jats:italic>c</jats:italic> = 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, <jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$$ 2\;\cdotp\;\mathbb{B} $$</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mn>2</mml:mn>
<mml:mspace />
<mml:mo>·</mml:mo>
<mml:mspace />
<mml:mi>B</mml:mi>
</mml:math>
</jats:alternatives>
</jats:inline-formula>, the triple covering of the largest Fischer group, 3 · Fi
<jats:sub>24</jats:sub>
<jats:sup>′</jats:sup>
and multiple-covering of the second largest Conway group, 2 · 2<jats:sup>1+22</jats:sup> · Co<jats:sub>2</jats:sub>. 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 <jats:italic>c</jats:italic> = 12 has the Conway group Co<jats:sub>0</jats:sub> ≃ 2 · Co<jats:sub>1</jats:sub> as an automorphism group.</jats:p>