Schedule Nov 17, 2020
A topological umbral moonshine conjecture
Theo Johnson-Freyd, Perimeter Inst.
Cite as: doi:10.26081/K63316

I will propose a "topological" description of M24 umbral moonshine. Specifically, I will describe a specific M24-equivariant SCFT, and explain that if it is M24-equivariantly nullhomotopic in the space of SQFTs — if it can be continuously deformed to an SQFT with spontaneous supersymmetry breaking — then that nullhomotopy would produce the mock modular forms of generalized M24-moonshine. I will not construct such a nullhomotopy, but I will provide some evidence of its existence: it is expected that the obstruction for and SQFT to be nullhomotopic is valued in a space of "topological modular forms", and I have calculated that the obstruction vanishes "perturbatively at odd primes". Time permitting, I will suggest that the "optimal growth condition" of umbral moonshine corresponds to working with "topological cusp forms", and I will outline a version of the construction for the umbral groups 2M12 and 2AGL3(2).

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