Citation: Kitaev, Alexei, and Liang Kong. "Models for gapped boundaries and domain walls." Communications in Mathematical Physics 313.2 (2012): 351-373.
Web: https://arxiv.org/abs/1104.5047
Tags: Defects/boundaries, Kitaev-quantum-double
This is an influential early paper about the algebraic theory of gapped boundaries and domain walls. The major point of the article is to take the algebraic theory of gapped boundaries which has been developing in the realm of conformal field theory and apply it to topological order. This means introducing a new physical mechanism for why boundaries should be described by module categories, which is specific to the Levin-Wen model.
The authors discuss the details of this proposal. In particular, they give focus to the fusion of domain walls, boundary defects, and the fusion of boundary defects. An important example which is stressed in this paper is the rough and smooth boundaries of the toric code, which were first discussed in
> Bravyi, Sergey B., and A. Yu Kitaev. "Quantum codes on a lattice with boundary." arXiv preprint quant-ph/9811052 (1998).