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## "Bulk-edge correspondence in (2+ 1)-dimensional abelian topological phases", Chetan Nayak, et al., 2014

*Reviewed September 6, 2023*

*Citation:* Cano, Jennifer, et al. "Bulk-edge correspondence in (2+ 1)-dimensional abelian topological phases." Physical Review B 89.11 (2014): 115116.

*Web:* https://arxiv.org/abs/1310.5708

*Tags:* Abelian-anyons, Defects/boundaries

This is the paper which first classified abelian anyonic theories.
They all decompose into prime theories, which fall into a few nice infinite families.

This is not the main result of this paper, however. The main study is between the bulk behavior
and the boundary behavior of a topological phase. The interesting phenomenon is that the same
bulk phase can have two different boundary phases.
As with most things in this area, the correspondence is intimately linked to quadratic forms,
and the theory of quadratic forms is used to explain the phenomenon in a rather complete fashion.

One interesting thing to keep in mind is that discrete gauge theories should
arise as symmetry breaking of infinite gauge theories. The groups Zn
are special because they arise as symmetry breaking of U(1) gauge theories.
This work shows that all abelian phases are represented by U(1)^N gauge theories,
as one might expect.