Remarks on 2+1 Self-dual Chern-Simons Gravity

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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Cited by in corpus (10)

• Noncommutative Topological Theories of Gravity
• Hamiltonian analysis of SO(4,1) constrained BF theory
• On S-duality in (2+1)-Chern-Simons Supergravity
• Hamiltonian dynamics and gauge symmetry for three-dimensional Palatini theory with cosmological constant
• Hamiltonian dynamics of an exotic action for gravity in three dimensions
• Corners of gravity: the case of gravity as a constrained BF theory
• A Vector Non-abelian Chern-Simons Duality
• S-duality for 2-d gravity
• BTZ entropy from topological M-theory
• New Reflections on Gravitational Duality