nLab
Yetter model

Context

\infty-Chern-Simons theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

Ingredients

Definition

Examples

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 Yetter model or Crane-Yetter model is a 4d TQFT sigma-model quantum field theory whose target space is a discrete 2-groupoid and whose background gauge field is a circle 4-bundle.

Together with the Dijkgraaf-Witten model these form the first two steps in filtering of target spaces by homotopy type truncation of ∞-Chern-Simons theory with discrete target spaces. It is hence also an example of a 4d Chern-Simons theory.

Properties

Relation to Turaev-Viro model on the boundary

The 3d TQFT Turaev-Viro model is a boundary field theory of the Yetter model (Barrett&Garci-Islas&Martins 04, theorem 2). Related discussion is in Freed4-3-2 8-7-6”.

Definition

Fix

The Yetter-model is the ∞-Dijkgraaf-Witten theory induced by this data.

References

The model without a background gauge field/cocycle was considered in

  • David Yetter, TQFTs from homotopy 2-types , Journal of Knot Theory and its Ramifications 2 (1993), 113-123.

The effect of having a nontrivial group 4-cocycle was considered (but now only on a 1-group) in

The reinterpretation of the “state sum” equation used in the above publications as giving homomorphisms of simplicial sets/topological spaces is given in

  • Tim Porter, Interpretations of Yetter’s notion of GG-coloring : simplicial fibre bundles and non-abelian cohomology, Journal of Knot Theory and its Ramifications 5 (1996) 687-720,

and then extended to colorings in homotopy n-types in

  • Tim Porter, Topological Quantum Field Theories from Homotopy n-types, Journal of the London Math. Soc. (2) 58 (1998) 723-732.

See also

  • João Faria Martins and Tim Porter, On Yetter’s invariants and an extension of the Dijkgraaf-Witten invariant to categorical groups, Theory and Applications of Categories, Vol. 18, 2007, No. 4, pp 118-150. (TAC)

which has some remarks about higher (2-)group cocycles towards the end.

Revised on October 6, 2013 22:31:00 by Urs Schreiber (195.37.209.182)