Jing-Yuan Chen, Finding the Missed Topological Operators in Lattice Models
Title: Finding the Missed Topological Operators in Lattice Models
Abstract: In both condensed matter physics and high energy physics, defining a quantum field theory on the lattice is important for various reasons: for concretely defining the theory, for deriving non-perturbative results, and for performing Monte-Carlo or other numerical computations. However, a crucial long standing problem is that the topological operators, which are important for non-perturbative physics, usually become ill-defined once the theory is put on the lattice. In some cases this problem has been resolved---the most notable example being the vortices in the Villain model, which led to the discovery of the BKT transition. However, in more general cases the problem is unresolved---the most notable example being the instanton in lattice QCD.
There is a deep reason behind the difficulty. I will show this long standing problem is---and has to be---solved by higher category theory. This seemingly formal mathematical language actually becomes very physically intuitive in the context of lattice models. A profound systematic relation between continuum QFT and lattice QFT is then revealed.