# Levin-Wen is a gauge theory: entanglement from topology

### APA

Kawagoe, K. (2024). Levin-Wen is a gauge theory: entanglement from topology. Perimeter Institute. https://pirsa.org/24020087

### MLA

Kawagoe, Kyle. Levin-Wen is a gauge theory: entanglement from topology. Perimeter Institute, Feb. 20, 2024, https://pirsa.org/24020087

### BibTex

@misc{ pirsa_PIRSA:24020087, doi = {10.48660/24020087}, url = {https://pirsa.org/24020087}, author = {Kawagoe, Kyle}, keywords = {Condensed Matter}, language = {en}, title = {Levin-Wen is a gauge theory: entanglement from topology}, publisher = {Perimeter Institute}, year = {2024}, month = {feb}, note = {PIRSA:24020087 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

The Levin-Wen model is known to produce a vast array of topological phases of matter. Among these theories are gauge theories such as the twisted quantum double. In this talk, we will show that the Levin-Wen model is itself a gauge theory. In particular, given a unitary fusion category C, we construct a globally tube algebra (Tube(C)) symmetric lattice model and gauge this symmetry to produce the Levin-Wen model with anyons described by the Drinfeld center Z(C). This construction endows the terms of the Levin-Wen Hamiltonian with the interpretation of flux and charge operators for the Tube(C) gauge symmetry. Furthermore, this construction gives a gauge theoretic interpretation to the mathematical fact that the category of representations of Tube(C) is equivalent to Z(C). To demonstrate this new class of Tube(C) symmetric theories, we will explicitly explore the case where C is the Fibonacci category Fib. We will write down the ungauged Tube(Fib) symmetric theory, compute the symmetry action, and show how to gauge the Tube(Fib) global symmetry to produce the double Fibonacci Levin-Wen model.

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