# Non-Invertible Theta Symmetries

### APA

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

### MLA

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

### BibTex

@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}} }

**Collection**

**Subject**

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