Non-invertible defects from the Conway SCFT to K3 sigma models

After the usual paper discussion, Roberta Angius will give a talk on the paper "Non-invertible defects from the Conway SCFT to K3 sigma models" (2504.18619).

"We initiate the study of supersymmetry-preserving topological defect lines (TDLs) in the Conway moonshine module Vf♮. We show that the tensor category of such defects, under suitable assumptions, admits a surjective but non-injective ring homomorphism into the ring of ℤ-linear maps of the Leech lattice into itself. This puts strong constraints on possible defects and their quantum dimensions. We describe a simple construction of non-invertible TDLs from orbifolds of holomorphic (super)vertex operator algebras, which yields non-trivial examples of TDLs satisfying our main theorem. We conjecture a correspondence between four--plane--preserving TDLs in Vf♮ and supersymmetry--preserving TDLs in K3 non-linear sigma models, which extends the correspondence between symmetry groups to the level of tensor category symmetry. We establish evidence for this conjecture by constructing non-invertible TDLs in special K3 non-linear sigma models."