Monstrous Moonshine & Quantum Gravity: Where Does 196883 Come From?

[tzimie]

I am reading this: https://en.wikipedia.org/wiki/Monstrous_moonshine
I understand where 196883 (196884) comes from in math.
But where does this constant appear in quantum gravity?

 

[mitchell porter]

According to a 2007 hypothesis of Witten, it would be the number of dimensions in the Hilbert space of a type of minimal "BTZ" black hole in 2+1 dimensions - minimal because purely gravitational, it's a scenario in which no other fields are present. The moonshine conjectures were proven by Borcherds using the "FLM" bosonic string, whose vibrations are restricted to a particular 24-dimensional space. If I understand correctly, these restrictions also prevent the string from having anything other than gravitational (spin-2) excitations, so it would be appropriate to model purely gravitational physics.

However, the 2007 idea has never quite been made to work (this might be the latest attempt). Maybe it requires bosonic M-theory compactified on the FLM space; who knows.

 

[jedishrfu]

I think it comes in via the duality of QG and extremal holomorphic CFTs under the assumption that the cosmological constant can be negative. If so then moonshine would be one such example:

{quote]
Conjectured relationship with quantum gravity
In 2007, E. Witten suggested that AdS/CFT correspondence yields a duality between pure quantum gravity in (2+1)-dimensional anti de Sitter space and extremal holomorphic CFTs. Pure gravity in 2+1 dimensions has no local degrees of freedom, but when the cosmological constant is negative, there is nontrivial content in the theory, due to the existence of BTZ black hole solutions. Extremal CFTs, introduced by G. Höhn, are distinguished by a lack of Virasoro primary fields in low energy, and the moonshine module is one example.
[/quote]

from the wikipedia article:
https://en.wikipedia.org/wiki/Monstrous_moonshine