Remarks on 2+1 Self-dual Chern-Simons Gravity
arXiv:hep-th/9906154 · doi:10.1103/PhysRevD.61.085022
Abstract
We study 2+1 Chern-Simons gravity at the classical action level. In particular we rederive the linear combinations of the ``standard'' and ``exotic'' Einstein actions, from the (anti) self-duality of the ``internal'' Lorentzian indices. The relation to a genuine four-dimensional (anti)self-dual topological theory greatly facilitates the analysis and its relation to hyperbolic three-dimensional geometry. Finally a non-abelian vector field ``dual'' action is also obtained.
16+1 pages, LaTeX file, no figures, clarifications and comments added, typos corrected and one reference added
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