Non-Invertible Theta Symmetries


Bhardwaj, L. (2023). Non-Invertible Theta Symmetries. Perimeter Institute. https://pirsa.org/23020035


Bhardwaj, Lakshya. Non-Invertible Theta Symmetries. Perimeter Institute, Feb. 07, 2023, https://pirsa.org/23020035


          @misc{ pirsa_PIRSA:23020035,
            doi = {10.48660/23020035},
            url = {https://pirsa.org/23020035},
            author = {Bhardwaj, Lakshya},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Non-Invertible Theta Symmetries},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {feb},
            note = {PIRSA:23020035 see, \url{https://pirsa.org}}

Lakshya Bhardwaj Harvard University


The modern point of view is that the global symmetries of a quantum field theory are described by topological defects/operators of the theory. In general such symmetries are non-invertible, i.e. the associated topological defects do not admit an inverse under fusion. I will describe a general construction of such non-invertible topological defects by coupling lower-dimensional topological quantum field theories (TQFTs) to discrete gauge fields living in a higher-dimensional bulk. The associated symmetries would be referred to as theta symmetries, as this construction can be understood as a generalization of the notion of theta angle. Mathematically, this construction is connected to interesting fusion higher-categories like those formed by higher-representations of groups and higher-groups. I will briefly explain this mathematical connection. I will also describe how the study of theta symmetries includes within it, as a special case, the study of topological phases of matter pursued in condensed matter physics. Towards the end of the talk, I will discuss some works in progress regarding possible physical applications of non-invertible symmetries. Based on ArXiv: 2212.06159, 2208.05973.

Zoom Link: https://pitp.zoom.us/j/92668739313?pwd=ZmdteFQybU9SbTlPNVQxV3l5dE5FQT09