Nonpropagation of massive mode on AdS2 in topologically massive gravity

TL;DR

This paper investigates topologically massive gravity on AdS2 using AO dimensional reduction, finding no propagating massive modes on AdS2 backgrounds, contrasting with KK reduction results.

Contribution

It demonstrates the absence of propagating massive modes in AdS2 within topologically massive gravity using AO reduction, highlighting differences from KK reduction.

Findings

No propagating massive mode on AdS2 background.

Different two-dimensional actions lead to non-equivalent on-shell amplitudes.

AdS2 vacua relate to AdS3 and warped AdS3 backgrounds.

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.