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ムーンシャイン予想関連
http://en.wikipedia.org/wiki/Monstrous_moonshine
Conjectured relationship with quantum gravity
Under Witten's proposal (Witten (2007)), gravity in AdS space with maximally negative cosmological constant is AdS/CFT dual to a holomorphic CFT with central charge c=24,
and the partition function of the CFT is precisely j-744, i.e., the graded character of the moonshine module.
Furthermore, they conjectured the existence of a family of twisted chiral gravity theories parametrized by elements of the monster,
suggesting a connection with generalized moonshine and gravitational instanton sums.
At present, all of these ideas are still rather speculative, in part because 3d quantum gravity does not have a rigorous mathematical foundation.