On exotic modular tensor categories
Seung-moon Hong, Eric Rowell, Zhenghan Wang

TL;DR
This paper investigates two exotic (2+1)-dimensional topological quantum field theories derived from subfactor theory, providing evidence they are counterexamples to the conjecture that all such theories are Chern-Simons-Witten theories, and explores their computational potential.
Contribution
It demonstrates that these two TQFTs are not among known mathematically constructed TQFTs and are not quantum doubles of braided fusion categories, suggesting they are exotic and potentially counterexamples to the conjecture.
Findings
The two TQFTs are not among known constructed TQFTs.
Neither TQFT is a quantum double of a braided fusion category.
Representation of braid groups can be used for universal quantum computation.
Abstract
It has been conjectured that every -TQFT is a Chern-Simons-Witten (CSW) theory labelled by a pair , where is a compact Lie group, and a cohomology class. We study two TQFTs constructed from Jones' subfactor theory which are believed to be counterexamples to this conjecture: one is the quantum double of the even sectors of the subfactor, and the other is the quantum double of the even sectors of the Haagerup subfactor. We cannot prove mathematically that the two TQFTs are indeed counterexamples because CSW TQFTs, while physically defined, are not yet mathematically constructed for every pair . The cases that are constructed mathematically include: 1. is a finite group--the Dijkgraaf-Witten TQFTs; 2. is torus ; 3. is a connected semi-simple Lie group--the Reshetikhin-Turaev TQFTs. We prove that the…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology
