Zesting produces modular isotopes and explains their topological invariants

2021/07/23 by Colleen Delaney, Delaney, Colleen, Sung Hoon Kim +3 · 1 citation
Physics and Astronomy · #18M15 #18M20 #18M30 #57K16 #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum many-body systems #Quantum, superfluid, helium dynamics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2107.11374

openalex publication_date 2021/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the ribbon zesting construction can produce modular isotopes -- different modular fusion categories with the same modular data. The result relies on the observation that the Reshetikhin-Turaev invariants of framed links associated to a ribbon fusion category satisfy a factorization property under zesting. This gives a new perspective on using topological invariants to classify topological order in light of modular data not being a complete invariant.

Citations

• Classical and quantum conformal field theory
• On two approaches to 3-dimensional TQFTs
• A Topological Invariant for Modular Fusion Categories

Cited by

• Zesting and the relative complexity of Reshetikhin-Turaev invariants

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