2011/08/31 by Domenico Fiorenza, Christopher L. Rogers, Urs Schreiber · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.1142/s0219887812500788
published as Int. J. Geom. Methods Mod. Phys. 10 (2013), no. 1, 1250078, 36 pp · We learned that an equivalent Chern-Weil description of AKSZ sigma-models is already presented in [arXiv:0711.4106] in the language of Q-manifolds. This result is now properly credited. We thank Alexei Kotov and Thomas Strobl for this remark
arxiv created 2012/06/09 · openalex publication_date 2012/10/16 · arxiv updated 2013/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Chern–Weil theory provides for each invariant polynomial on a Lie algebra 𝔤 a map from 𝔤-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.