Comments on Non-Invertible Symmetries in K3 CFTs and the Conway Moonshine Module

There is an established connection between discrete symmetry groups of K3 non-linear sigma models and a distinguished N=1 chiral SCFT called the Conway moonshine module. More specifically, all symmetry groups of K3 NLSMs preserving the N=4 superconformal algebra can be obtained as subgroups of “Conway zero”, the group of symmetries of the Conway module, and their explicit action on the BPS spectrum can (almost always) be obtained via traces in the Conway module. A natural question is whether this relation extends to fusion category symmetry of these theories. I will discuss positive evidence in this direction, by exploring examples of non-invertible topological defect lines in K3 NLSMs and the Conway module. This is based on work in progress with R. Angius, S. Giaccari, and R. Volpato.

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Zoom link: https://harvard.zoom.us/j/97784644596
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