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"Symmetry fractionalization, defects, and gauging of topological phases", Maissam Barkeshli, Parsa Bonderson, Meng Cheng, Zhenghan Wang, 2019

Reviewed October 6, 2023

Citation: Barkeshli, Maissam, et al. "Symmetry fractionalization, defects, and gauging of topological phases." Physical Review B 100.11 (2019): 115147.

Web: https://arxiv.org/abs/1410.4540

Tags: Foundational, Defects/boundaries, SPT/SETs

This is a big paper, detailing a theory of how global symmetries of topological orders can be gauged into local symmetries. Phases of matter equivalent in the absence of the symmetry but distinct in the presence of symmetry are known as symmetry-protected topological phases (SPT phases), and serve a key role in the modern theory of topological order.

This theory is very mathematically intricate, and as such there are lots of mathematical appendices and reviews included in this article to be maximally palatable to a physics audience.

There is a huge amount of information in this paper, and it serves as the foundation for the rest of the algebraic theory of SPT phases.

Various aspects of the theory had already been exposited in papers before this. For example, gauging was treated thoroughly in

> Cui, Shawn X., et al. "On gauging symmetry of modular categories." Communications in Mathematical Physics 348.3 (2016): 1043-1064.