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Journal Article

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

MPS-Authors

Bojowald,  Martin
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0406445.pdf
(Preprint), 242KB

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Citation

Bojowald, M., Kotov, A., & Strobl, T. (2005). Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries. Journal of Geometry and Physics, 54(4), 400-426. Retrieved from http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ8-4F29J0R-1&_user=42783&_handle=V-WA-A-W-D-MsSWYWW-UUA-U-AAVUZABBVA-AABYAEVAVA-ZUZWVZDDA-D-U&_fmt=summary&_coverDate=08%2F31%2F2005&_rdoc=3&_orig=browse&_srch=%23toc%235304%232005%23999459995%23596539!&_cdi=5304&view=c&_acct=C000003518&_version=1&_urlVersion=0&_userid=42783&md5=c81599f113977603d3a69b7c8fd8217c.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4DEF-D
Abstract
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.