12:45
Great progress has been made recently in exploiting categorical/topological/higher symmetries in quantum field theory. I will explain how the same structure is realised directly in the lattice models of statistical mechanics, generalizing Kramers-Wannier duality to a wide class of models. In particular, I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse lattice topological defects in two and 1+1 dimensions. These defects possess a variety of remarkable properties. Not only is the partition function is independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice. I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.