Enriched string-net models and their excitations

Abstract

Boundaries of Walker-Wang models have been used to construct commuting projector models which realize chiral unitary modular tensor categories (UMTCs) as boundary excitations. Given a UMTC $\mathcal{A}$ representing the Witt class of an anomaly, the article [arXiv:2208.14018] gave a commuting projector model associated to an $\mathcal{A}$-enriched unitary fusion category $\mathcal{X}$ on a 2D boundary of the 3D Walker-Wang model associated to $\mathcal{A}$. That article claimed that the boundary excitations were given by the enriched center/Müger centralizer $Z^{\mathcal{A}}(\mathcal{X})$ of $\mathcal{A}$ in $Z(\mathcal{X})$. In this article, we give a rigorous treatment of this 2D boundary model, and we verify this assertion using topological quantum field theory (TQFT) techniques, including skein modules and a certain semisimple algebra whose representation category describes boundary excitations. We also use TQFT techniques to show the 3D bulk point excitations of the Walker-Wang bulk are given by the Müger center $Z_2(\mathcal{A})$, and we construct bulk-to-boundary hopping operators $Z_2(\mathcal{A})\to Z^{\mathcal{A}}(\mathcal{X})$ reflecting how the UMTC of boundary excitations $Z^{\mathcal{A}}(\mathcal{X})$ is symmetric-braided enriched in $Z_2(\mathcal{A})$. This article also includes a self-contained comprehensive review of the Levin-Wen string net model from a unitary tensor category viewpoint, as opposed to the skeletal $6j$ symbol viewpoint.

arXiv comment43 pages; numerous figures

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Cited by in corpus (9)

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• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Enriched monoidal categories I: centers
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Local topological order and boundary algebras
• Dualities between 2+1d fusion surface models from braided fusion categories
• Condensation Completion and Defects in 2+1D Topological Orders
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly