Symmetry as shadow of topological order


Wen, X. (2021). Symmetry as shadow of topological order. Perimeter Institute. https://pirsa.org/21030001


Wen, Xiao-Gang. Symmetry as shadow of topological order. Perimeter Institute, Mar. 08, 2021, https://pirsa.org/21030001


          @misc{ pirsa_21030001,
            doi = {},
            url = {https://pirsa.org/21030001},
            author = {Wen, Xiao-Gang},
            keywords = {Condensed Matter},
            language = {en},
            title = {Symmetry as shadow of topological order},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {mar},
            note = {PIRSA:21030001 see, \url{https://pirsa.org}}


Recently, the notion of symmetry has been extended from 0-symmetry described by group to higher symmetry described by higher group. In this talk, we show that the notion of symmetry can be generalized even further to "algebraic higher symmetry". Then we will describe an even more general point of view of symmetry, which puts the (generalized) symmetry charges and topological excitations at equal footing: symmetry can be viewed gravitational anomaly, or symmetry can be viewed as shadow topological order in one higher dimension.