nLab anyonic topological order via braided fusion categories -- references

Anyonic topological order in terms of braided fusion categories

Anyonic topological order in terms of braided fusion categories

Claim and status

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 is:

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

Further discussion (mostly review and mostly without attribution):

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:

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:

In string/M-theory

Arguments realizing such anyonic topological order in the worldvolume-field theory on M5-branes:

Via KK-compactification on closed 3-manifolds (Seifert manifolds) analogous to the 3d-3d correspondence (which instead uses hyperbolic 3-manifolds):

Via 3-brane defects:

Further discussion

Relation to ZX-calculus:

On detection of topological order by observing modular transformations on the ground state:

See also:

Last revised on June 6, 2024 at 16:36:44. See the history of this page for a list of all contributions to it.