Some universal properties of Levin-Wen models

TL;DR

This paper reviews universal properties of Levin-Wen models, including boundary-bulk duality and defect correspondence, and presents new insights into boundary excitations and the functoriality of the monoidal center.

Contribution

It introduces new results on boundary excitation properties and conjectures on the functoriality of the monoidal center within Levin-Wen models.

Findings

Universal boundary-bulk duality identified

Duality-defect correspondence established

Detailed analysis of boundary excitations provided

Abstract

We review the key steps of the construction of Levin-Wen type of models on lattices with boundaries and defects of codimension 1,2,3 in a joint work with Alexei Kitaev. We emphasize some universal properties, such as boundary-bulk duality and duality-defect correspondence, shared by all these models. New results include a detailed analysis of the local properties of a boundary excitation and a conjecture on the functoriality of the monoidal center.