On Maximal Massive 3D Supergravity

We construct, at the linearized level, the three-dimensional (3D) N = 4 supersymmetric "general massive supergravity" and the maximally supersymmetric N = 8 "new massive supergravity". We also construct the maximally supersymmetric linearized N = 7 topologically massive supergravity, although we expect N = 6 to be maximal at the non-linear level.Comment: 33 page

Lorentz Violation of Quantum Gravity

A quantum gravity theory which becomes renormalizable at short distances due to a spontaneous symmetry breaking of Lorentz invariance and diffeomorphism invariance is studied. A breaking of Lorentz invariance with the breaking patterns $SO(3,1)\to O(3)$ and $SO(3,1)\to O(2)$, describing 3+1 and 2+1 quantum gravity, respectively, is proposed. A complex time dependent Schr\"odinger equation (generalized Wheeler-DeWitt equation) for the wave function of the universe exists in the spontaneously broken symmetry phase at Planck energy and in the early universe, uniting quantum mechanics and general relativity. An explanation of the second law of thermodynamics and the spontaneous creation of matter in the early universe can be obtained in the symmetry broken phase of gravity.Comment: 10 pages, minor change and reference added. Typos corrected. To be published in Class. Quant. Grav

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

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

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

A spin-4 analog of 3D massive gravity

A 6th-order, but ghost-free, gauge-invariant action is found for a 4th-rank symmetric tensor potential in a three-dimensional (3D) Minkowski spacetime. It propagates two massive modes of spin 4 that are interchanged by parity, and is thus a spin-4 analog of linearized "new massive gravity". Also found are ghost-free spin-4 analogs of linearized "topologically massive gravity" and "new topologically massive gravity", of 5th- and 8th-order respectively.Comment: 16 pages, v2 : version published in Class. Quant. Gra

Killing Vector Fields in Three Dimensions: A Method to Solve Massive Gravity Field Equations

Killing vector fields in three dimensions play important role in the construction of the related spacetime geometry. In this work we show that when a three dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the ricci tensor. Using this property we give ways of solving the field equations of Topologically Massive Gravity (TMG) and New Massive Gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three dimensional symmetric tensors of the geometry, the ricci and einstein tensors, their covariant derivatives at all orders, their products of all orders are completely determined by the Killing vector field and the metric. Hence the corresponding three dimensional metrics are strong candidates of solving all higher derivative gravitational field equations in three dimensions.Comment: 25 pages, some changes made and some references added, to be published in Classical and Quantum Gravit

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

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