Brown-Henneaux's canonical approach to topologically massive gravity

Abstract

We analyze the symmetry realized asymptotically on the two dimensional boundary of AdS 3 geometry in topologically massive gravity, which consists of the gravitational Chern-Simons term as well as the usual Einstein-Hilbert and negative cosmological constant terms. Our analysis is based on the conventional canonical method and proceeds along the line completely parallel to the original Brown and Henneaux's. In spite of the presence of the gravitational Chern-Simons term, it is confirmed by the canonical method that the boundary theory actually has the conformal symmetry satisfying the left and right moving Virasoro algebras. The central charges of the Virasoro algebras are computed explicitly and are shown to be left-right asymmetric due to the gravitational Chern-Simons term. It is also argued that the Cardy's formula for the BTZ black hole entropy capturing all higher derivative corrections agrees with the extended version of the Wald's entropy formula. The M5-brane system is illustrated as an application of the present calculation.

Mass and angular momentum of black holes in 3D gravity theories with first order formalism

“…These results are also the same with [7,8]. The charge variation (43) can be re-expressed by a total variation form.…”

“…We can also read the symplectic potential Θ from the variation of the Lagrangian and calculate Noether charge using (8),…”

“…The linearization of this theory describes the existence of a single massive graviton mode. This theory also allows some black hole solutions having Ad S asymptotics [7,8]. There have been many investigations for this TMG theory from the viewpoint of Ad S/C FT correspondence [9][10][11][12].…”

Fake gaps in AdS3/CFT2

“…The role of this term is to induce a gravitational anomaly. In particular for a space-time that is asymptotically AdS 3 the gravitational Chern-Simons term induces an unbalance in the central charges given by [38][39][40][41] …”

Some properties of the de Sitter black holes in three dimensional spacetime

“…It is well known that the gravity theory with the cosmological constant and gravitational Chern-Simons term (topologically massive gravity; TMG) has massive graviton modes and black hole solutions, such as BTZ and warped AdS black holes [1,2,3,4,5,6,7,8,9]. A few years ago, Bergshoeff, Hohm and Townsend have introduced a new gravity theory, so-called new massive gravity (NMG), that consists of the Einstein-Hilbert term, cosmological constant and higher curvature terms which have a specific combination of the square of the Ricci scalar and the square of the Ricci tensor [10,11,12,13].…”