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arXiv · 1707.08887

Geometric actions for three-dimensional gravity

Glenn Barnich·Hernan A. Gonzalez·Patricio Salgado-Rebolledo
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Abstract

The solution space of three-dimensional asymptotically anti-de Sitter or flat Einstein gravity is given by the coadjoint representation of two copies of the Virasoro group in the former and the centrally extended BMS$_3$ group in the latter case. Dynamical actions that control these solution spaces are usually constructed by starting from the Chern-Simons formulation and imposing all boundary conditions. In this note, an alternative route is followed. We study in detail how to derive these actions from a group-theoretical viewpoint by constructing geometric actions for each of the coadjoint orbits, including the appropriate Hamiltonians. We briefly sketch relevant generalizations and potential applications beyond three-dimensional gravity.

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Glenn Barnich, Hernan A. Gonzalez, Patricio Salgado-Rebolledo. 2017-07-27. Geometric actions for three-dimensional gravity. https://doi.org/10.1088/1361-6382%2Faa9806

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