Non-invertible symmetries on the lattice (1/2)

Abstract: Recently, the study of generalized symmetries and their applications has been rapidly developing. In particular, examples of a class of generalized symmetry called "non-invertible symmetries" have been found in four dimensions. The key idea in this development is the "topological defects." An approach to such generalized symmetry and topological defects is through the lattice theory approach developed by Aasen, Mong, and Fendley. In this lecture, I will explain this AMF approach and the generalization to four dimensions done by Koide, Nagoya, and myself. I will start with one-dimensional systems and explain the relation between classical statistical mechanics and quantum mechanics as well as operators and defects. Then, I will turn to two dimensions and explain the Kramerse-Wannier duality and its manifestation by non-invertible topological defects. Finally, I will explain our own work on the topological defects in the four dimensional Z2 lattice gauge theory.

MathematicsPhysics

Audience: researchers in the topic

SNU String Seminar