[Special Seminar] Non-invertible defects from the Conway SCFT to K3 sigma model

by Roberta Angius (IFT - Madrid)

Wednesday 2 Jul 2025, 11:30 → 13:00 Europe/Berlin

3009 (Notkestrasse 9)

Recently, symmetries have been reinterpreted in terms of topological operators supported on codi-
mension 1 submanifolds of spacetime and satisfying group-like and invertible fusion rules. This has
naturally led to the notion of generalized symmetries as categories of topological defects supported
on arbitrary codimension submanifolds with possibly non-invertible fusion rules.
In this talk, I will present first results toward the classification of topological defects that commute
with the spectral flow and the N = (4, 4) superconformal symmetry in two dimensional non-linear
sigma models on K3, as well as those that preserve supersymmetry in the Conway superconformal
field theory V f ♮. By analyzing the induced action of these defects on the lattice of RR D-brane
charges in the K3 models, and on a particular embedding of the Leech lattice into the space of
Ramond ground states in the Conway theory, I will extract a number of parallel structural results
for the respective categories of topological defects.
These findings lead me to conjecture a correspondence between four-plane-preserving topological
defect lines (TDLs) in V f ♮ and supersymmetry-preserving TDLs in K3 non-linear sigma models.
This correspondence extends the known relation between the symmetry groups of the two theories
to a deeper equivalence at the level of their tensor categorical symmetries.