Geometric actions for three-dimensional gravity

G. Barnich, H. A. González, P. Salgado-Rebolledo

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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 BMS3 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.

Original languageEnglish
Article number014003
JournalClassical and Quantum Gravity
Issue number1
StatePublished - 11 Jan 2018
Externally publishedYes


  • AdS/CFT correspondence
  • Chern-Simons theories
  • three-dimensional gravity


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