Lie algebroid morphisms, Poisson sigma models, and off-shell closed gauge symmetries

Martin Bojowald, Alexei Kotov, Thomas Strobl

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

Chern-Simons (CS) gauge theories in three dimensions and the Poisson sigma model (PSM) in two 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 the off-shell gauge symmetries as left action of some finite-dimensional Lie algebroid. Our approach allows us 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 the standard YM theory, gerbes, and the PSM.

Original languageEnglish (US)
Pages (from-to)400-426
Number of pages27
JournalJournal of Geometry and Physics
Volume54
Issue number4
DOIs
StatePublished - Aug 2005

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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