Recent progress in the symmetry/topological order correspondence

Abstract: In this talk, we discuss some recent progress in the symmetry/topological order correspondence. The correspondence basically says that topological aspects of a discrete symmetry in d dimensions are captured by topological data in a topological order in d+1 dimensions. The topological aspects of symmetry include but are not limited to symmetry charges, defects, their fusion rules as well as commutation relations. We will discuss (1) how a beyond-Landau transition is solved using the correspondence (arXiv: 2205.06244) and (2) in practice how we derive a topological order for a given symmetry in a 1+1d conformal field theory (arXiv:2106.02069). For the latter, two cases are particularly interesting: (i) when the symmetry is anomalous, (ii) after the CFT is matched with a topological order, there is a further symmetry that enriches the topological order. If time allowed, we discuss the similarities and relations of our setting with that proposed by Freed, Moore, and Teleman.

HEP - phenomenologyHEP - theorymathematical physicscategory theory

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.