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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.