Abstract
We consider the recently proposed exotic 3D massive gravity. We show that this theory has a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying either the standard Brown-Henneaux boundary conditions or the weakened asymptotic behavior of the so-called Log-gravity. Both sectors contain non-Einstein spaces with SO(2) × mathbb{R} isometry group, showing that the Birkhoff theorem does not hold all over the parameter space, even if strong AdS boundary conditions are imposed. Some of these geometries correspond to 3D black holes dressed with a Log-gravity graviton. We conjecture that such geometries appear in a curve of the parameter space where the exotic 3D massive gravity on AdS3 is dual to a chiral conformal field theory. The theory also contains other interesting vacua, including different families of non-AdS black holes.
Highlights
NMG, present a consistency problem when discussed in the context of Anti de-Sitter (AdS)/CFT
We consider the recently proposed exotic 3D massive gravity. We show that this theory has a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying either the standard Brown-Henneaux boundary conditions or the weakened asymptotic behavior of the so-called Log-gravity
Both sectors contain non-Einstein spaces with SO(2) × R isometry group, showing that the Birkhoff theorem does not hold all over the parameter space, even if strong AdS boundary conditions are imposed. Some of these geometries correspond to 3D black holes dressed with a Log-gravity graviton. We conjecture that such geometries appear in a curve of the parameter space where the exotic 3D massive gravity on AdS3 is dual to a chiral conformal field theory
Summary
The one we will mainly focus on solutions to (1.1)–(1.2) when the following relation among the parameters is satisfied μ m2l − m2l2. We will refer to (2.1) as the critical point (or, more precisely, the chiral curve) When this relation is obeyed, the theory exhibits quite special features: the linear excitations around AdS3 become massless [19] and low-decaying logarithmic modes appear. This can be observed at non-linear level by studying gravitational wave solutions on AdS3 of the type analyzed in [20,21,22]. Where is the D’Alambertian operator associated to the metric (2.2) This value of M± exactly agrees with the mass of the modes obtained by the linearized analysis of [19]. We will discuss these logarithmically decaying solutions in more detail
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