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My question concerns applications of monstrous moonshine, which is the connection between the $j$-function and the monster group. Recently, physicists have applied it to string theory and, ultimately, to a possible form of 3D quantum gravity, as seen in the article below:

http://www.quantamagazine.org/20150312-mathematicians-chase-moonshines-shadow/

However, my question is what are other applications of monstrous moonshine to physics outside string theory? Are there possible connections to conformal field theories in condensed matter physics? If not to condensed matter, what are some other possible physical applications?

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    $\begingroup$ So far you are none for zero because string theory is not even false, yet. In other words, it is not canonical physics by any means. It is not clear to me how or why one would even want to apply a discrete group of such size to a condensed matter application which does not have more than a handful of approximate symmetries, at most (and truthfully, most condensed matter physics problems of interest are actually about the question of what happens when the symmetry breaks on dislocations etc.). $\endgroup$ – CuriousOne Jun 3 '15 at 6:48

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