Topologically massive gravity on AdS$_2$ spacetimes

Details Topologically massive gravity on AdS$_2$ spacetimes Topologically massive gravity on AdS$_2$ spacetimes

2009-01-15

arxiv.org/abs/0901.2141v2

JHEP 0906:043,2009

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 3 figures, added appendix, version to appear in JHEP

Scientific paper

10.1088/1126-6708/2009/06/043

We study the topologically massive gravity with a negative cosmological constant on AdS$_2$ spacetimes by making use of dimensional reduction. For a constant dilaton, this two-dimensional model admits three AdS$_2$ vacuum solutions, which are related to AdS$_3$ and warped AdS$_3$ with an identification upon uplifting three dimensions. We carry out the perturbation analysis around these backgrounds to find what is a physically propagating field. It turns out that a mode of $\delta F = (h-f/e)$ is merely a redundant field of dilaton $\varphi$ in the absence of Chern-Simons terms, while it becomes a massive scalar in the presence of Chern-Simons terms. This shows clearly that the proper number of physically propagating degrees of freedom is one for the topologically massive gravity. Moreover, at the points of $K=l,l/3$, $\delta F$ becomes a massless scalar which implies that there is no physically propagating degrees of freedom at the chiral point.

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