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According to https://en.wikipedia.org/wiki/Hierarchy_problem#Finite_Groups.

Hierarchy problem can be theoretically solved using symmetry of certain bosonic string theory on the Leech lattice (though there is not even a single citation in that paragraph). So my question is this: Whether hierarchy problem is also addressed in LQG since both the theories (ST and LGQ) tries to address quantization of gravity.

This question might be wrong as well. As https://arxiv.org/abs/gr-qc/9710008 states that one cannot calculate mass of elementary particle in LQG and wikipedia article about hierarchy problem states that it ultimately boils down to discrepancy between Higgs boson mass and Planck mass. So above question may be ill-posed for LQG.

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  • $\begingroup$ In string theory the Hierarchy problem is solved by Supersymmetry. $\endgroup$ – Rexcirus Oct 29 '18 at 23:20
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Unless there have been new developments in LQG that I am unaware of, electroweak gauge theories are not embedded (as of yet, there may be internal progress) and therefore the Hierarchy problem itself would not be appreciated by the theory.

Furthermore, the theoretical approach to the hierarchy problem with sporadic groups and leech lattices is very hand wavy (SO FAR) and lacks the rigour of the canonical and “new approaches” to the problem. Some have gone so far as to say the coincidences of the approach are numerology, although I am not so sure.

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  • $\begingroup$ Who actually proposes to obtain the hierarchy from the order of the Monster group? Wikipedia gives no source. $\endgroup$ – Mitchell Porter Dec 14 '19 at 3:54
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    $\begingroup$ (1) ptep-online.com/2011/PP-27-11.PDF seems to approach some type of motivation, whether or not this work is worth consideration I’m unsure— i haven’t read it myself. (2) arxiv.org/abs/1908.11032 is titled “flavour moonshine” and uses modular forms (and maybe moonshine?) as a motivation. I haven’t paid much attention to this line of work so I’m not qualified to judge the validity of these papers or if the “monster” approach to EW hierarchy has even been formulated beyond the wikipedia page. $\endgroup$ – Alexander Nordal Dec 14 '19 at 7:03
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    $\begingroup$ @MitchellPorter if this work proves to be useful in obtaining some hierarchy— how exactly the symmetries would “shut off” at the electroweak scale, or some other (more arbitrary) scale, without being some feature of a wilsonian EFT with natural cutoff at the scale parameter of the theory I can’t imagine. If thats the case, the program has not resolved the hierarchy problem but just made it more convoluted in my opinion. regardless, i really don’t know enough about the program to make a sensible comment on it all. $\endgroup$ – Alexander Nordal Dec 14 '19 at 7:23
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    $\begingroup$ Even if the monster were somehow involved in phenomenology, neither paper even mentions the idea of explaining the magnitude of the hierarchy via the order of the monster group, let alone shows how that would work. Indeed, I can't think of any natural way whereby the order of a group is related to a ratio of energy scales. The latter idea really does seem to be pure numerology. $\endgroup$ – Mitchell Porter Dec 14 '19 at 12:20

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