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On the Boundary Dynamics of Chern-Simons Gravity

Giovanni Arcioni·Matthias Blau·Martin O'Loughlin
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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.

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Giovanni Arcioni, Matthias Blau, Martin O'Loughlin. 2002-12-16. On the Boundary Dynamics of Chern-Simons Gravity. https://doi.org/10.1088/1126-6708%2F2003%2F01%2F067

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