For semisimple Lie algebra targets
For discrete group targets
For discrete 2-group targets
For Lie 2-algebra targets
For targets extending the super Poincare Lie algebra
(such as the supergravity Lie 3-algebra, the supergravity Lie 6-algebra)
Chern-Simons-supergravity
for higher abelian targets
for symplectic Lie n-algebroid targets
for the $L_\infty$-structure on the BRST complex of the closed string:
higher dimensional Chern-Simons theory
topological AdS7/CFT6-sector
functorial quantum field theory
Reshetikhin?Turaev model? / Chern-Simons theory
FQFT and cohomology
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
The 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.
The Yetter model is not the same as the Crane-Yetter model.
Fix
$G$ a discrete 2-group; write $\mathbf{B}G$ for its delooping 2-groupoid;
$\alpha : \mathbf{B}G \to \mathbf{B}^4 U(1)$ a characteristic class with coefficients in the circle 4-group. This is equivalently a cocycle in degree $4$ group cohomology
The Yetter-model is the ∞-Dijkgraaf-Witten theory induced by this data.
The model without a background gauge field/cocycle was considered in
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) .
The reinterpretation of the “state sum” equation used in the above publications as giving homomorphisms of simplicial sets/topological spaces is given in
and then extended to colorings in homotopy n-types in
See also
which has some remarks about higher (2-)group cocycles towards the end.