-Chern-Simons theory ∞ \infty Quantum field theory
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
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 Freed “ 4-3-2 8-7-6”. Definition
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
D. Birmingham, M. Rakowski,
On Dijkgraaf-Witten Type Invariants, Lett. Math. Phys. 37 (1996), 363.
Marco Mackaay, Spherical 2-categories and 4-manifold invariants, Adv. Math. 153 (2000), no. 2, 353–390. ( arXiv:math/9805030) .
John Barrett, J. Garcia-Islas, João Faria Martins, Observables in the Turaev-Viro and Crane-Yetter models, J. Math. Phys. 48:093508, 2007 ( arXiv:math/0411281)
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 , Journal of Knot Theory and its Ramifications 5 (1996) 687-720, -coloring : simplicial fibre bundles and non-abelian cohomology G G
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.
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