categorical-braiding-subfactor

name	categorical-braiding-subfactor
description	Braiding structures on categorical multi-interval Jones-Wassermann subfactor planar algebras from unitary modular fusion categories. Constructs braidings inducing projective unitary representations of balanced superelliptic mapping class groups, encoding higher-genus topological data. New proof of subfactor self-duality. Activation: braiding structures, Jones-Wassermann subfactor, planar algebra, modular fusion category, mapping class group, higher-genus topology, categorical quantum
metadata	{"arxiv_id":"2607.08296","published":"2026-07-09","authors":"Multiple authors","tags":["quantum","category-theory","subfactor","braiding","topology","modular-fusion"]}

Categorical Braiding Structures on Subfactors

Methodology

Constructs braiding structures on multi-interval Jones-Wassermann subfactor planar algebra from any unitary modular fusion category.

Core Results

1. Braiding construction: On multi-interval Jones-Wassermann subfactor planar algebra from unitary modular fusion category
2. Self-duality proof: New proof using the braiding construction
3. Mapping class group representation: Braidings induce projective unitary representation of balanced superelliptic mapping class group
4. Higher-genus encoding: Structures encode non-trivial higher-genus data of underlying category

Mathematical Framework

• Unitary modular fusion category: Input data for construction
• Planar algebra: Multi-interval Jones-Wassermann subfactor structure
• Braiding: Categorical braiding on the planar algebra
• Mapping class group: Balanced superelliptic mapping class group representation

Workflow

1. Start with unitary modular fusion category
2. Construct multi-interval Jones-Wassermann subfactor planar algebra
3. Define braiding structures on the planar algebra
4. Verify self-duality via braiding
5. Extract projective unitary representation of mapping class group

Pitfalls

• Modular fusion requirement: Input must be a unitary modular fusion category (not just fusion category)
• Multi-interval complexity: Construction significantly more complex than single-interval case
• Higher-genus subtlety: Encoding higher-genus data requires careful treatment of boundary conditions

Related Skills

• topological-quantum-computing (topological structures)
• quantum-error-correction-methods (subfactor theory in QEC)
• tensor-cookbook-diagrams (planar algebra diagrams)