We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali-Gabadadze-Porrati model, cascading gravity and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware-Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally we present alternative and related models of massive gravity such as new massive gravity, Lorentz-violating massive gravity and non-local massive gravity.

Massive Gravity

These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.

Holographic Duality with a View Toward Many-Body Physics

We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We review the duality between gravitational backgrounds and the various states of quantum matter which live on the boundary. We then describe quantum matter at a fixed commensurate density (often described by conformal field theories), and also compressible quantum matter with variable density, providing an extensive discussion of transport in both cases. We present a unified discussion of the holographic theory of transport with memory matrix and hydrodynamic methods, allowing a direct connection to experimentally realized quantum matter. We also explore other important challenges in non-quasiparticle physics, including symmetry broken phases such as superconductors and non-equilibrium dynamics.

Holographic Quantum Matter

We explore the space of static solutions of the recently discovered three-dimensional ``new massive gravity'' (NMG), allowing for either sign of the Einstein-Hilbert term and a cosmological term parametrized by a dimensionless constant $\ensuremath{\lambda}$. For $\ensuremath{\lambda}=\ensuremath{-}1$ we find black hole solutions asymptotic (but not isometric) to the unique (anti) de Sitter [(A)dS] vacuum, including extremal black holes that interpolate between this vacuum and $(\mathrm{A}){\mathrm{dS}}_{2}\ifmmode\times\else\texttimes\fi{}{S}^{1}$. We also investigate unitarity of linearized NMG in (A)dS vacua. We find unitary theories for some dS vacua, but (bulk) unitarity in AdS implies negative central charge of the dual conformal field theories (CFT), except for $\ensuremath{\lambda}=3$ where the central charge vanishes and the bulk gravitons are replaced by ``massive photons.'' A similar phenomenon is found in the massless limit of NMG, for which the linearized equations become equivalent to Maxwell's equations.

/pdf/more-on-massive-3d-gravity-1r8ywyggol.pdf

More on Massive 3D Gravity

We study charged dilaton black branes in AdS
 4. Our system involves a dilaton ϕ coupled to a Maxwell field F
 μν
 with dilaton-dependent gauge coupling, $ \frac{1}{{{g^2}}} = {f^2}\left( \phi \right) $
 . First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where f(ϕ) = e
 αϕ
 , are Lifshitz-like, with a dynamical exponent z determined by α. The black hole thermodynamics varies in an interesting way with α, but in all cases the entropy is vanishing and the specific heat is positive for the near extremal solutions. We then compute conductivity in these backgrounds. We find that somewhat surprisingly, the AC conductivity vanishes like ω
 2 at T = 0 independent of α. We also explore the charged black brane physics of several other classes of gauge-coupling functions f(ϕ). In addition to possible applications in AdS/CMT, the extremal black branes are of interest from the point of view of the attractor mechanism. The near horizon geometries for these branes are universal, independent of the asymptotic values of the moduli, and describe generic classes of endpoints for attractor flows which are different from AdS
 2 × R
 2.

/pdf/holography-of-charged-dilaton-black-holes-3jskgerxaq.pdf

Holography of Charged Dilaton Black Holes

A pioneering treatise presenting how the new mathematical techniques of holographic duality unify seemingly unrelated fields of physics. This innovative development morphs quantum field theory, general relativity and the renormalisation group into a single computational framework and this book is the first to bring together a wide range of research in this rapidly developing field. Set within the context of condensed matter physics and using boxes highlighting the specific techniques required, it examines the holographic description of thermal properties of matter, Fermi liquids and superconductors, and hitherto unknown forms of macroscopically entangled quantum matter in terms of general relativity, stars and black holes. Showing that holographic duality can succeed where classic mathematical approaches fail, this text provides a thorough overview of this major breakthrough at the heart of modern physics. The inclusion of extensive introductory material using non-technical language and online Mathematica notebooks ensures the appeal to students and researchers alike.

Holographic Duality in Condensed Matter Physics

We consider a higher derivative gravity theory in four dimensions with a negative cosmological constant and show that vacuum solutions of both Lifshitz type and Schrodinger type with arbitrary dynamical exponent z exist in this system. Then we find an analytic black hole solution which asymptotes to the vacuum Lifshitz solution with z = 3/2 at a specific value of the coupling constant. We analyze the thermodynamic behavior of this black hole and find that the black hole has zero entropy while non-zero temperature, which is very similar to the case of BTZ black holes in new massive gravity at a specific coupling. In addition, we find that the three dimensional Lifshitz black hole recently found by E. Ayon-Beato et al. has a negative entropy and mass when the Newton constant is taken to be positive.

https://iopscience.iop.org/article/10.1088/1126-6708/2009/10/080/pdf

A Lifshitz Black Hole in Four Dimensional R**2 Gravity

In this note we study the properties of linearized gravitational excitations in the new massive gravity theory in asymptotically AdS(3) spacetime and find that there is also a critical point for the mass parameter at which massive gravitons become massless as in topological massive gravity in AdS(3). However, at this critical point in the new massive gravity the energy of all branches of highest weight gravitons vanish and the central charges also vanish within the Brown-Henneaux boundary conditions. The new massive gravity in asymptotically AdS(3) spacetime seems to be trivial at this critical point under the Brown-Henneaux boundary conditions if the Brown-Henneaux boundary conditions can be consistent with this theory. At this point, the boundary conditions of log gravity may be preferred.

http://iopscience.iop.org/article/10.1088/1126-6708/2009/04/106/pdf

Note on new massive gravity in AdS(3)

In this note we study the boundary conditions for the new massive gravity theory in asymptotically AdS3 spacetime. We find that the Brown-Henneaux boundary conditions are consistent with the new massive gravity for all any value of the mass parameter. At the critical point where the central charge vanishes, the conserved charges vanish, too. This provides further evidence that the theory may be trivial at the critical point under Brown-Henneaux boundary conditions. The log boundary conditions are also examined and we find that we can have three kinds of log boundary conditions for this new massive gravity theory, each of which could be consistent at the critical point, while for other value of the mass parameter, the log gravity boundary condition is not consistent.

http://iopscience.iop.org/article/10.1088/1126-6708/2009/05/039/pdf

Yan Liu

Papers

Holographic Duality in Condensed Matter Physics

A Lifshitz Black Hole in Four Dimensional R**2 Gravity

Note on new massive gravity in AdS(3)

Consistent boundary conditions for new massive gravity in AdS(3)

The holographic Weyl semi-metal