Eur. Phys. J. C (2010) 67: 533-541
https://doi.org/10.1140/epjc/s10052-010-1333-3

Regular Article - Theoretical Physics

Nonpropagation of massive mode on AdS₂ in topologically massive gravity

¹ Institute of Basic Science and School of Computer Aided Science, Inje University, Gimhae, 621-749, Korea
² Department of Physics and Center for Quantum Spacetime, Sogang University, Seoul, 121-742, Korea

^* e-mail: ywkim65@gmail.com

Received: 18 September 2009
Revised: 1 March 2010
Published online: 19 May 2010

Abstract

Making use of Achucarro–Ortiz (AO) type of dimensional reduction, we study the topologically massive gravity with a negative cosmological constant on AdS₂ spacetimes. For a constant dilaton, this two-dimensional model also admits three AdS₂ vacuum solutions, which are related to two AdS₃ and warped AdS₃ backgrounds with an identification upon uplifting three dimensions. We carry out the perturbation analysis around these backgrounds to find what is a physically propagating field. However, it turns out that there is no propagating massive mode on AdS₂ background, in contrast to the Kaluza–Klein (KK) type of dimensional reduction. We note that two dimensionally reduced actions are different and thus, the non-equivalence of their on-shell amplitudes is obtained.