Nonpropagation of massive mode on AdS2 in topologically massive gravity

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.