On Critical Massive (Super)Gravity in adS3

We review the status of three-dimensional "general massive gravity" (GMG) in its linearization about an anti-de Sitter (adS) vacuum, focusing on critical points in parameter space that yield generalizations of "chiral gravity". We then show how these results extend to N=1 super-GMG, expanded about a supersymmetric adS vacuum, and also to the most general `curvature-squared' N=1 supergravity model.Comment: 10 pages, Proceedings of ERE 2010, Granada, 6-10 september 2010; reference adde

Holographic two-point functions for 4d log-gravity

We compute holographic one- and two-point functions of critical higher-curvature gravity in four dimensions. The two most important operators are the stress tensor and its logarithmic partner, sourced by ordinary massless and by logarithmic non-normalisable gravitons, respectively. In addition, the logarithmic gravitons source two ordinary operators, one with spin-one and one with spin-zero. The one-point function of the stress tensor vanishes for all Einstein solutions, but has a non-zero contribution from logarithmic gravitons. The two-point functions of all operators match the expectations from a three-dimensional logarithmic conformal field theory.Comment: 35 pages; v2: typos corrected, added reference; v3: shorter introduction, minor changes in the text in section 3, added reference; published versio

Short-cut to new anomalies in gravity duals to logarithmic conformal field theories

Various massive gravity theories in three dimensions are conjecturally dual to logarithmic conformal field theories (LCFTs). We summarise the status of these conjectures. LCFTs are characterised by the values of the central charges and the so-called "new anomalies". We employ a short-cut to calculate these new anomalies in generalised massive gravity and in the recently proposed higher-derivative gravity theories with holographic c-theorem. Both cases permit LCFTs exhibiting intriguing features, like rank three Jordan cells or non-zero central charges. Finally, as an example we discuss in some detail the partially massless version of new massive gravity, a theory with several special properties that we call "partially massless gravity".Comment: 34 pages, 2 figures; v2: added references; v3: Several rewordings in the introduction and section 2, added references. Matches published versio

More on Massive 3D Supergravity

Completing earlier work on three dimensional (3D) N=1 supergravity with curvature-squared terms, we construct the general supergravity extension of cosmological massive gravity theories. We expand about supersymmetric anti-de Sitter vacua, finding the conditions for bulk unitarity and the critical points in parameter space at which the spectrum changes. We discuss implications for the dual conformal field theory.Comment: v1 : 53 pages, 1 figure; v2 : significantly shortened, 42 p., version published in Class. Quant. Gra

Holographic Renormalization and Stress Tensors in New Massive Gravity

We obtain holographically renormalized boundary stress tensors with the emphasis on a special point in the parameter space of three dimensional new massive gravity, using the so-called Fefferman-Graham coordinates with relevant counter terms. Through the linearized equations of motion with a standard prescription, we also obtain correlators among these stress tensors. We argue that the self-consistency of holographic renormalization determines counter terms up to unphysical ambiguities. Using these renormalized stress tensors in Fefferman-Graham coordinates, we obtain the central charges of dual CFT, and mass and angular momentum of some $AdS$ black hole solutions. These results are consistent with the previous ones obtained by other methods. In this study on the Fefferman-Graham expansion of new massive gravity, some aspects of higher curvature gravity are revealed.Comment: Version accepted for publication in JHEP, conclusion revised, references adde

Cosmological Topologically Massive Gravitons and Photons

We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS_3 backgrounds are not only shifted from their flat background values but, more surprisingly, split according to chirality. For all finite values of the topological mass, we find a single bulk degree of freedom with positive energy, and exhibit a complete set of normalizable, finite-energy wave packet solutions. This model can also be written as a sum of two higher-derivative SL(2,R) Chern--Simons theories, weighted by the central charges of the boundary conformal field theory. At two particular "critical" values of the couplings, one of these central charges vanishes, and linearized topologically massive gravity becomes equivalent to topologically massive electromagnetism; however, the physics of the bulk wave packets remains unaltered here.Comment: 36 pages, 1 figure. v2: Expanded; exhibits localized normalizable wave packets and exact chiral pp-wave solutions. v3: Added references; clarification on bulk vs. boundary chirality. v4: Published version; changes include discussion of bulk solutions' asymptotic acceptability at all m

A Complete Classification of Higher Derivative Gravity in 3D and Criticality in 4D

We study the condition that the theory is unitary and stable in three-dimensional gravity with most general quadratic curvature, Lorentz-Chern-Simons and cosmological terms. We provide the complete classification of the unitary theories around flat Minkowski and (anti-)de Sitter spacetimes. The analysis is performed by examining the quadratic fluctuations around these classical vacua. We also discuss how to understand critical condition for four-dimensional theories at the Lagrangian level.Comment: 20 pages, v2: minor corrections, refs. added, v3: logic modified, v4: typos correcte

Warped black holes in 3D general massive gravity

We study regular spacelike warped black holes in the three dimensional general massive gravity model, which contains both the gravitational Chern-Simons term and the linear combination of curvature squared terms characterizing the new massive gravity besides the Einstein-Hilbert term. The parameters of the metric are found by solving a quartic equation constrained by an inequality that imposes the absence of closed timelike curves. Explicit expressions for the central charges are suggested by exploiting the fact that these black holes are discrete quotients of spacelike warped AdS(3) and a known formula for the entropy. Previous results obtained separately in topological massive gravity and in new massive gravity are recovered as special cases.Comment: 38 pages, 7 figures. v2: minor changes, added refs and an appendix on self-dual and null z-warped black hole

On higher derivative gravity, c-theorems and cosmology

We consider higher derivative gravity lagrangians in 3 and 4 dimensions, which admit simple c-theorems, including upto six derivative curvature invariants. Following a suggestion by Myers, these lagrangians are restricted such that the fluctuations around (anti) de Sitter spaces have second order linearized equations of motion. We study c-theorems both in the context of AdS/CFT and cosmology. In the context of cosmology, the monotonic function is the entropy defined on the apparent horizon through Wald's formula. Exact black hole solutions which are asymptotically (anti) de Sitter are presented. An interesting lower bound for entropy is found in de Sitter space. Some aspects of cosmology in both D=3 and D=4 are discussed.Comment: 23 pages, v3: clarifications added, references adde