A Functorial Theory of Defects in Abelian Chern-Simons Theory

arXiv:2609.21414 · math-ph, cond-mat.str-el, hep-th, math.MP, math.QA · Submitted 2026-09-18 · Read on arXiv

math-ph, cond-mat.str-el, hep-th, math.MP, math.QA

Submitted: 2026-09-18

Updated: 2026-09-18

Terminology

• Quantization — 13× in this paper · explained in 12 episodes
• Domain Walls — 11× in this paper · explained in 2 episodes
• Topological Order — 8× in this paper · explained in 2 episodes
• Holonomy — 7× in this paper · explained in 2 episodes
• Hilbert Space — 6× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Axioms — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Degeneracy — 2× in this paper · explained in 3 episodes
• Modularity — 2× in this paper · explained in 9 episodes
• Anyon Condensation — 1× in this paper · explained in 1 episode
• Anyons — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Topological Defects — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Turaev-Viro invariants as an extended TQFT III
• Classification of abelian spin Chern-Simons theories
• Classification of Extended Abelian Chern-Simons Theories
• Equivalence of Extended $U(1)$ Chern-Simons and Reshetikhin-Turaev TQFTs
• Equivalence of toral Chern-Simons and Reshetikhin-Turaev theories
• A Rigorous Functional-Integral Construction of Toral Chern-Simons Theory
• Toral Chern-Simons TQFT via Geometric Quantization in Real Polarization
• Torus Berry Data Determine All-Genus Abelian Topological Orders
• Turaev-Viro invariants as an extended TQFT
• Alterfold Topological Quantum Field Theory
• Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories
• Reshetikhin-Turaev construction and $\mathrm{U}(1)^n$ Chern-Simons partition function

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