Non-invertible anomalies and Topological orders


Ji, W. (2019). Non-invertible anomalies and Topological orders. Perimeter Institute. https://pirsa.org/19110125


Ji, Wenjie. Non-invertible anomalies and Topological orders. Perimeter Institute, Nov. 19, 2019, https://pirsa.org/19110125


          @misc{ pirsa_19110125,
            doi = {10.48660/19110125},
            url = {https://pirsa.org/19110125},
            author = {Ji, Wenjie},
            keywords = {Condensed Matter},
            language = {en},
            title = {Non-invertible anomalies and Topological orders},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110125 see, \url{https://pirsa.org}}

Wenjie Ji Massachusetts Institute of Technology (MIT)

Talk Type Scientific Series


It has been realized that anomalies can be classified by topological phases in one higher dimension. Previous studies focus on ’t Hooft anomalies of a theory with a global symmetry that correspond to invertible topological orders and/or symmetry protected topological orders in one higher dimension. In this talk, I will introduce an anomaly that appears on the boundaries of (non-invertible) topological order with anyonic excitations [1]. The anomalous boundary theory is no longer invariant under a re-parametrization of the same spacetime manifold. The anomaly is matched by simple universal topological data in the bulk, essentially the statistics of anyons. The study of non-invertible anomalies opens a systematic way to determine all gapped and gapless boundaries of topological orders, by solving simple eigenvector problems. As an example, we find all conformal field theories (CFT) of so-called ``minimal models’’, except four cases, can be the critical boundary theories of Z_2 topological order (toric code). The matching of non-invertible anomaly have wide applications. For example, we show that the gapless boundary of double-semion topological order must have central charge c_L=c_R >= 25/28. And the gapless boundary of the non-Abelian topological order described by S_3 topological quantum field theory can be three-state Potts CFT, su(2)_4 CFT, etc. [1] WJ, Xiao-Gang Wen, arXiv: 1905.13279, Phys. Rev. Research 1,033054