TY - JOUR

T1 - Geometric actions for three-dimensional gravity

AU - Barnich, G.

AU - González, H. A.

AU - Salgado-Rebolledo, P.

N1 - Funding Information:
We thank Andrés Gomberoff, Daniel Grumiller, Wout Merbis and Blagoje Oblak for useful discussions. GB is grateful to Fondecyt (Chile) Grant N°1141309 for support during his visit to Chile where part of this work was completed. GB is supported by the Fund for Scientific Research-FNRS (Belgium) (convention FRFC PDR T.1025.14 and convention IISN 4.4503.15), HG is supported by the Austrian Science Fund (FWF), project P 28751-N2, and P S-R is supported by the Fondecyt (Chile) Grant N°3160581.
Publisher Copyright:
© 2017 IOP Publishing Ltd.

PY - 2018/1/11

Y1 - 2018/1/11

N2 - 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.

AB - 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.

KW - AdS/CFT correspondence

KW - Chern-Simons theories

KW - three-dimensional gravity

UR - http://www.scopus.com/inward/record.url?scp=85038618621&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/aa9806

DO - 10.1088/1361-6382/aa9806

M3 - Article

AN - SCOPUS:85038618621

VL - 35

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 1

M1 - 014003

ER -