Categorical symmetry — applications in 1+1D

Speaker:  Arkya Chatterjee

Date:    2022.11.22

Time:   09:30-11:00

Tencent Meeting: 607 3645 0351

      

Abtract:

Symmetries are among the most important tools in the toolkit of a theoretical physicist. In the context of condensed matter physics, there is a long tradition of using symmetry to label and distinguish different phases of matter. The notion of symmetry becomes particularly rich in quantum systems; we now understand that symmetries come in various shapes and forms: anomaly-free, ('t Hooft) anomalous, higher-form, higher group, algebraic/non-invertible etc. All of these adjectives for symmetry may be unified, at least for finite symmetries, using the mathematical formalism of topological order in one higher dimension. We call this unified framework categorical symmetry. This categorical unification of symmetry has various applications in different contexts. In this talk, I will present two applications for 1+1D lattice models: identifying dualities and obtaining constraints on global phase diagrams. In the first part, I will discuss how the algebra of local symmetric operators encodes information about its categorical symmetry thereby leading us to dualities between different symmetry descriptions. In the second part, I will discuss how the relationship between boundary theories of 2+1D topological order helps us constrain the global phase diagram of 1+1D theories with finite symmetry. (Based on: arXiv:2203.03596 and 2205.06244)

 

[Category and Topological Order Seminar]