2004/06/22 by Martin Bojowald, Alexei Kotov, Thomas Strobl · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.1016/j.geomphys.2004.11.002
published as J.Geom.Phys. 54 (2005) 400-426 · 24 pages
arxiv created 2004/06/22 · openalex publication_date 2004/12/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Chern-Simons gauge theories in 3 dimensions and the Poisson Sigma Model (PSM) in 2 dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids and their symmetries (on-shell) as homotopies of such morphisms. We point out that the (off-shell) gauge symmetries of the PSM in the literature are not globally well-defined for non-parallelizable Poisson manifolds and propose a covariant definition of them as left action of some finite-dimensional Lie algebroid. Our approach allows to avoid complications arising in the infinite dimensional super-geometry of the BV- and AKSZ-formalism. This preprint is a starting point in a series of papers meant to introduce Yang-Mills type gauge theories of Lie algebroids, which include and generalize the standard YM theory, the PSM, and gerbes.