Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries

Details Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries

2004-06-22

arxiv.org/abs/math/0406445v1

J.Geom.Phys. 54 (2005) 400-426

Mathematics

Differential Geometry

24 pages

Scientific paper

10.1016/j.geomphys.2004.11.002

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.

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