Citation: Fuchs, Jurgen, Christoph Schweigert, and Alessandro Valentino. "Bicategories for boundary conditions and for surface defects in 3-d TFT" Communications in Mathematical Physics 321 (2013): 543-575.
Web: https://arxiv.org/abs/1203.4568
Tags: Modular-tensor-categories, Defects/boundaries, TQFT
In this paper, the authors give a systematic way of thinking about boundary theories for non-doubled topological phases. The idea is that every bulk anyon should be able to fuse to a boundary defect. This gives a functor from the category of bulk anyons to the category of boundary defects. The important observation of this paper is that this condensation functor has the structure of a central functor. That is, every condensed anyon naturally comes with the structure of a half-braiding. This means that every condensed anyon naturally gives an element of the Drinfeld center of the category of boundary defects! They then argue that this functor gives an equivalence of categories.
They phrase this a TQFT language, where instead of bringing anyons to the boundary they imagine bringing Wilson lines to the boundary. This approach is inspired by an earlier paper which did what this paper does, but for abelian Chern-Simons theory:
> Kapustin, Anton, and Natalia Saulina. "Topological boundary conditions in abelian Chern-Simons theory." Nuclear Physics B 845.3 (2011): 393-435.
> Kapustin, Anton, and Natalia Saulina. "Surface operators in 3d topological field theory and 2d rational conformal field theory." Mathematical foundations of quantum field theory and perturbative string theory 83 (2011): 175-198.
This paper has other nice discussion as well, as well as mathematical overview, which makes it potentially a good first reference for the theory of gapped boundaries/domain walls in the non-doubled case.