Symmetry topological field theory and generalised Kramers–Wannier dualities

by Clément Delcamp (IHES)

Friday Nov 8, 2024, 2:00 PM → 3:00 PM Europe/Paris

112 (Bat. Braconnier)

Given finite group generalisations of the celebrated Ising model, I will explore aspects of their realisations as boundary theories of a three-dimensional topological quantum field theory. I will then consider two operations: gauging an arbitrary subsymmetry and performing Fourier transforms of the local weights encoding the dynamics of the theory. Both operations can be carried out in terms of the three-dimensional topological quantum field theory. Whenever the whole symmetry is gauged, combining both operations recovers the non-abelian Kramers–Wannier duals à la Freed and Teleman. Motivated by this example, I will discuss generalisations of these operations for a class of two-dimensional Euclidean lattice field theories admitting topological lines encoded into a spherical fusion category.