A higher Chern–Weil derivation of AKSZ σ-models

Chern-Weil theory provides for each invariant polynomial on a Lie algebra a map from connections to differential cocycles whose volume holonomy is the corresponding Chern-Simons theory action functional. Kotov and Strobl have observed that this naturally generalizes from Lie algebras to dg-manifolds and to dg-bundles and that the Chern-Simons action functional associated this way to an n-symplectic manifold is the action functional of the AKSZ σ-model whose target space is the given n-symplectic manifold (examples of this are the Poisson σ-model or the Courant σ-model, including ordinary Chern-Simons theory, or higher-dimensional Abelian Chern-Simons theory). Here we show how, within the framework of the higher Chern-Weil theory in smooth ∞-groupoids, this result can be naturally recovered and enhanced to a morphism of higher stacks, the same way as ordinary Chern-Simons theory is enhanced to a morphism from the stack of principal G-bundles with connections to the 3-stack of line 3-bundles with connections. © 2013 World Scientific Publishing Company. © 2013 World Scientific Publishing Company.