Maths HEP Lunchtime Seminars: Topological Defects on the Lattice
4 March 2016 13:00 in CM221
I describe work with David Aasen and Roger Mong on the construction of topological defects in two-dimensional classical lattice models and one-dimensional quantum chains. The defects satisfy commutation relations guaranteeing the partition function depends only on topological properties of the defects. One useful consequence is a generalization of Kramers-Wannier duality to a wide class of height models, applicable on any surfaces. Another is an explicit definition of twisted boundary conditions that yield the precise shift in momentum quantization, and hence the spin of the associated conformal field. I describe the close connection between microscopic and macroscopic properties; for example the splitting and joining properties of these defect lines are exactly those of chiral operators in conformal field theory and topological quantum field theory.