Topologically massive gravity on AdS$_2$ spacetimes

TL;DR

This paper investigates topologically massive gravity on AdS$_2$ spacetimes, revealing the nature of propagating modes and degrees of freedom, especially at special points like the chiral point, through dimensional reduction and perturbation analysis.

Contribution

It provides a detailed analysis of propagating modes in topologically massive gravity on AdS$_2$, clarifying the role of Chern-Simons terms and identifying the conditions for massless and massive scalars.

Findings

One propagating degree of freedom in general.

Massless scalar modes at specific points like $K=l,l/3$.

No propagating degrees of freedom at the chiral point.

Abstract

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.