On the Boundary Dynamics of Chern-Simons Gravity

Abstract

We study Chern-Simons theory with a complex G_C or a real G x G gauge group on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a G_C/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, for (E/A)dS gravity, the boundary action is a WZW model with target space (E/A)dS_3, reminiscent of a worldsheet for worldsheet mechanism. We discuss in some detail the properties of the boundary theories that arise and we confront our results with various related constructions in the literature.

22 pages, LaTeX2e, v2: JHEP3.cls, references and a footnote added

References in corpus (3)

• De Sitter Gravity and Liouville Theory
• Holography and the Polyakov action
• Dwelling on de Sitter

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• The covariant action of higher spin black holes in three dimensions
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• A note on the Hamiltonian structure of transgression forms
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