nLab unitary fusion category

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Contents

Idea

A unitary fusion category is a C*-fusion category.

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References

General

Anyonic topological order in terms of braided fusion categories

In condensed matter theory it is folklore that species of anyonic topological order correspond to braided unitary fusion categories/modular tensor categories.

The origin of the claim may be:

Early accounts re-stating this claim (without attribution):

Further discussion (all without attribution):

Relation to ZX-calculus:

Emphasis that the expected description of anyons by braided fusion categories had remained folklore, together with a list of minimal assumptions that would need to be shown:

Exposition and review:

  • Sachin Valera, A Quick Introduction to the Algebraic Theory of Anyons, talk at CQTS Initial Researcher Meeting (Sep 2022) [[pdf]]

See also:

  • Liang Kong, Topological Wick Rotation and Holographic Dualities, talk at CQTS (Oct 2022) [[pdf]]

An argument that the statement at least for SU(2)-anyons does follow from an enhancement of the K-theory classification of topological phases of matter to interacting topological order:

Last revised on June 7, 2022 at 19:46:35. See the history of this page for a list of all contributions to it.