Citation: Green, David, et al. "Enriched string-net models and their excitations." Quantum 8 (2024): 1301.
Web: https://arxiv.org/abs/2305.14068
Tags: Higher-dimensional, Kitaev-quantum-double, Modular-tensor-categories
This paper shows how to construct a lattice model for a general gapped boundary theory on a bulk Walker-Wang model. The construction is nice for several reasons. Firstly, their language is entirely category-theoretic - they never use F symbols or R symbols, and instead work entirely within the language of monoidal category string diagrams. Another reason is that their paper is nice is that they make some explicit calculations for the space of irreducible localized excitations, and demonstrate using the language of tube/dome algebras that they have the right algebraic structure (namely, Drinfeld center/centralizer).
For anyone wanting a decisive first-principles reference for why the bulk anyons of the Levin-Wen model are given by the Drinfeld center, or especially for the general statement about boundaries of non-trivial Walker-Wang models, this is the place to go. Note though that they aren't fully general about their derivation because they restrict themselves to small numbers of lattice sites for simplicity, but this is only a technical restriction.
For me, one of the most useful features of this paper is the model (due to Corey Jones) presented in Remark 3.5. This is a version of the Levin-Wen model which can be seen as the boundary of the Walker-Wang model with Z(X) as input, on the X-boundary, for some unitary fusion category X. The vertex excitations are now localized to violations of single terms in the Hamiltonian. This version of the Levin-Wen model is particularly useful for the sort of projects I'm working on these days.
This paper can be seen as a lattice-model companion paper to the following more purely high energy physics/category theory paper:
> Huston, Peter, et al. "Composing topological domain walls and anyon mobility." SciPost Physics 15.3 (2023): 076.