nLab
Crane-Yetter model

Contents

Context

Quantum field theory

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

The Crane-Yetter model is a 4d TQFT, not to be confused with the Yetter model.

It was defined originally as a state sum in State-Sum Invariants of 4-Manifolds. One labels the elements of a triangulation with objects and morphisms of a ribbon fusion category, usually the representation category of a quasitriangular Hopf algebra, or quantum group.

(The Yetter model, on the contrary, is defined for a finite 2-group.)

Relation to Turaev-Viro model on the boundary

The 3d TQFT Turaev-Viro model is a boundary field theory of the Crane-Yetter model (Barrett&Garcia-Islas&Martins 04, theorem 2).

As a fully extended TQFT

It can be understood as an extended topological quantum field theory, see 4-3-2 8-7-6.

Relation to BF-theory and Dijkgraaf-Witten theory

It is expected that the classical limit of the Crane-Yetter TQFT is BF theory. See John Baez’s article. A state sum model like the Crane-Yetter model, but with a classical Lie group, would be the Ooguri model?. We could understand the Crane-Yetter as a Dijkgraaf-Witten theory with a quantum group instead of a classical group, whereas the Yetter model is a Dijkgraaf-Witten theory with a 2-group. See also this blog post.

Last revised on November 18, 2014 at 23:34:32. See the history of this page for a list of all contributions to it.