Topological defects on the lattice
This course introduces topological defects in two-dimensional classical lattice models and quantum chains. The defects satisfy local commutation relations guaranteeing that the partition function is independent of their path. These relations and their solutions are extended to allow defect lines to fuse, branch and satisfy all the properties of a fusion category. It is shown how the two-dimensional classical lattice models and their topological defects are naturally described by boundary conditions of a Turaev-Viro-Barrett-Westbury partition function. These defects allow Kramers-Wannier duality to be generalized to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum.
Lecturer
Date
17th September ~ 26th November, 2021
Reference
1) https://arxiv.org/abs/1601.07185
2) https://arxiv.org/abs/2008.08598
2) https://arxiv.org/abs/2008.08598
Video Public
No
Notes Public
No
Lecturer Intro
Associate Professor, research interests are string theory, quantum field theory and topological field theory.