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).
**

**
**

To download: Right-click and choose "Save Link As..."

To begin viewing slides, click on the first slide below. (Or, view as pdf.)