An article of ours
A higher Chern-Weil derivation of AKSZ -models
Int. J. Geom. Methods Mod. Phys. 10 (2013) 1250078
in the context of ∞-Chern-Simons theory.
Chern-Weil theory provides for each invariant polynomial on a Lie algebra a map from -connections to differential cocycles whose volume holonomy is the the corresponding Chern-Simons theory action functional. We observe that in the context of higher Chern-Weil theory in smooth ∞-groupoids this statement generalizes from Lie algebras to L-∞ algebras and further to L-∞ algebroids. It turns out that the symplectic form on a symplectic higher Lie algebroid (for instance a Poisson Lie algebroid or a Courant Lie 2-algebroid) is ∞-Lie-theoretically an invariant polynomial. We show that the higher Chern-Simons action functional associated to this by higher Chern-Weil theory is the action functional of the AKSZ sigma-model with target space the given -algebroid (for instance the Poisson sigma-model or the Courant sigma-model).
Higher Chern-Weil Derivation of AKSZ Sigma-Models
and conference meetings
The corresponding preprint appeared a little later:
Meanwhile also (arXiv:0711.4106) had appeared, with similar observations.
The construction of the refined -Chern-Weil homomorphism, hence the Lie integration of these -algebraic constructions to circle n-bundles with connection on smooth ∞-stacks was finally accomplished in
This is what the above article is based on.
For more related references see also differential cohomology in a cohesive topos -- references.