We construct background-independent Noether charges in Topologically Massive Gravity with negative cosmological constant using its first-order formulation. The procedure is carried out by keeping track of the surface terms in the variation of the action, regardless the value of the gravitational Chern-Simons coupling $μ$. In particular, this method provides a definition of conserved quantities for solutions at the chiral point $μl = 1$ ($l$ is the AdS radius) that contain logarithmic terms (Log Gravity). It is also shown that the charge formula gives a finite result for warped AdS black holes without the need for any background-substraction procedure.
We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann-Cartan-Weyl space-times in arbitrary dimensions. We demonstrate the procedure of Weyl gauging on two examples in particular: General relativity, and topologically massive gravity in three dimensions.
We define conserved gravitational charges in -cosmologically extended- topologically massive gravity, exhibit them in surface integral form about their de-Sitter or flat vacua and verify their correctness in terms of two basic types of solution.
We study the conserved charges of supersymmetric solutions in the topologically massive gravity theory for both asymptotically flat and constant curvature geometries.
We study van Dam-Veltman-Zakharov discontinuity in the topologically new massive gravity (TNMG). The reduction from 2 degrees of freedom to one is interpreted as van Dam-Veltman-Zakharov discontinuity appeared when going from anti-de Sitter spacetime to Minkowski spacetime in the linearized TNMG.
I review how "classical SUGRA" embeddability establishes positive energy E for D=3 topologically massive gravity (TMG), with or without a cosmological term, a procedure familiar from D=4 Einstein gravity (GR). It also provides explicit expressions for E. In contrast to GR, E is not manifestly positive, due to the peculiar two-term nature of TMG.
We present an exact solution in 3-dimensional topologically massive gravity with negative cosmological constant which dynamically interpolates between a past horizon and a chiral AdS pp-wave. Similarly, upon time reversal, one obtains an AdS pp-wave with a future event horizon
The solution of topologically massive gravity with cosmological constant is reduced, for space-times with two commuting Killing vectors, to a special-relativistic dynamical problem. This approach is applied to the construction of a class of exact sourceless, horizonless solutions asymptotic to the BTZ extreme black holes.
We construct a "Chern-Simons-like" action for N=1 Topologically Massive Supergravity from the Chern-Simons actions of N=1 Supergravity and Conformal Supergravity. We convert this action into Hamiltonian form and use this to demonstrate that the theory propagates a single massive (2, 3/2) supermultiplet.
Wolfgang Kummer was a pioneer of two-dimensional gravity and a strong advocate of the first order formulation in terms of Cartan variables. In the present work we apply Wolfgang Kummer's philosophy, the `Vienna School approach', to a specific three-dimensional model of gravity, cosmological topologically massive gravity at the chiral point. Exploiting a new Chern-Simons representation we perform a canonical analysis. The dimension of the physical phase space is two per point, and thus the theory exhibits a local physical degree of freedom, the topologically massive graviton.
Using the principles of the modern scattering amplitudes programme, we develop a formalism for constructing the amplitudes of three-dimensional topologically massive gauge theories and gravity. Inspired by recent developments in four dimensions, we construct the three-dimensional equivalent of $x$-variables for conserved matter currents coupled to topologically massive gauge bosons or gravitons. Using these, we bootstrap various matter-coupled gauge-theory and gravitational scattering amplitudes, and conjecture that topologically massive gauge theory and topologically massive gravity are relat…
We construct, and establish the (covariant) conservation of, a 4-index "super-stress tensor" for TMG. Separately, we discuss its invalidity in quadratic curvature models and suggest a generalization.
We determine the black hole quasi-normal mode spectrum for tensor perturbations in topologically massive AdS-gravity. In the special case of chiral gravity quasi-normal modes are absent despite of the presence of a horizon. In the process we uncover a simple algebraic structure in the quasi normal modes spectrum: the tower of QNM's consists of descendents of a "chiral highest weight'' QNM which in turn satisfies a first order equation.
We calculate the one loop partition function for topologically massive higher spin gravity (TMHSG) for arbitrary spin by taking the spin-3 TMHSG action constructed in arXiv:1107.0915 and subsequently generalising it for an arbitrary spin. We find that the final result can be put into a product form which cannot be holomorphically factorized giving strong evidence that the topologically massive higher spin gravity is dual to a high spin extension of logarithmic CFT rather than a chiral one.
We calculate the free energy from the on-shell action for topologically massive gravity with negative and vanishing cosmological constant, thereby providing a first principles derivation of the free energy of Banados-Teitelboim-Zanelli (BTZ) black holes and flat space cosmologies. We summarize related recent checks of flat space holography.
At a critical ``chiral'' coupling, topologically massive gravity with a negative cosmological constant exhibits several unusual features, including the emergence of a new logarithmic branch of solutions and a linearization instability for certain boundary conditions. I show that at this coupling, the linearized theory may be parametrized by a free scalar field at the Breitenlohner-Freedman bound, and use this description to investigate these features.
We construct a Weyl-invariant extension of topologically massive gravity which, remarkably, turns out to include topologically massive electrodynamics, with a Proca mass term, conformally coupled to a scalar field. The action has no dimensionful parameters, therefore, the masses are generated via symmetry breaking either radiatively in flat backgrounds or spontaneously in constant curvature backgrounds. The broken phase of the theory, generically, has a single massive spin-2 and a massive spin-1 excitation. Chiral gravity in asymptotically anti-de Sitter spacetimes does not arise as a low ener…
We re-derive, compactly, a TMG decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We can then generalize it to include matter, which is necessarily null.
We construct two classes of exact solutions to the field equations of topologically massive electrodynamics coupled to topologically massive gravity in 2 + 1 dimensions. The self-dual stationary solutions of the first class are horizonless, asymptotic to the extreme BTZ black-hole metric, and regular for a suitable parameter domain. The diagonal solutions of the second class, which exist if the two Chern-Simons coupling constants exactly balance, include anisotropic cosmologies and static solutions with a pointlike horizon.
We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.
We compute the tree-level scattering amplitude between two covariantly conserved sources in generic Cosmological Topologically Massive Gravity augmented with a Fierz-Pauli term that has three massive degrees of freedom. We consider the Chiral Gravity limit in the anti-de Sitter space as well as the limit of Flat-Space Chiral Gravity. We show that Chiral Gravity cannot be unitarily deformed with a Fierz-Pauli mass. We calculate the non-relativistic potential energy between two point-like spinning sources. In addition to the expected mass-mass and spin-spin interactions, there are mass-spin inte…
We apply the Lee-Wald covariant phase space method to the Weyl-invariant Topologically Massive Gravity and compute the corresponding on-shell conserved charges. By using appropriate decay conditions for the existing propagating modes in the near-horizon of a stationary black hole, we obtain the charges generating the asymptotic symmetries. We show that the charges are integrable and the (modified) algebras among the asymptotic generators are closed for the certain choice of central extensions.
We show that an analytical continuation of the Vuorio solution to three-dimensional topologically massive gravity leads to a two-parameter family of black hole solutions, which are geodesically complete and causally regular within a certain parameter range. No observers can remain static in these spacetimes. We discuss their global structure, and evaluate their mass, angular momentum, and entropy, which satisfy a slightly modified form of the first law of thermodynamics.
We show that cosmological topologically massive gravity at the chiral point allows not only Brown-Henneaux boundary conditions as consistent boundary conditions, but slightly more general ones which encompass the logarithmic primary found in 0805.2610 as well as all its descendants.
We introduce a natural set of asymptotic conditions in the spacelike stretched AdS sector of topologically massive gravity. The Poisson bracket algebra of the canonical generators is shown to have the form of the semi-direct sum of a $u(1)$ Kac-Moody and a Virasoro algebra, with central charges. Using the Sugawara construction, we prove that the asymptotic symmetry coincides with the conformal symmetry, described by two independent Virasoro algebras with central charges. The result is in complete agreement with the hypothesis made in [6].
We give a detailed account of the free field spectrum and the Newtonian limit of the linearized "massive" (Pauli-Fierz), "topologically massive" (Einstein-Hilbert-Chern-Simons) gravity in 2+1 dimensions about a Minkowski spacetime. For a certain ratio of the parameters, the linearized free theory is Jordan-diagonalizable and reduces to a degenerate "Pais-Uhlenbeck" oscillator which, despite being a higher derivative theory, is ghost-free.
Three-dimensional topologically massive AdS gravity has a complicated constraint algebra, making it difficult to count nonperturbative degrees of freedom. I show that a new choice of variables greatly simplifies this algebra, and confirm that the theory contains a single propagating mode for all values of the mass parameter and the cosmological constant. As an added benefit, I rederive the central charges and conformal weights of the boundary conformal field theory from an explicit analysis of the asymptotic algebra of constraints.
The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights obtained in this direction over the last decade and apply the new techniques to Topologically Massive Gravity. We show that this theory is dual to a non-unitary CFT for any value of its parameter mu and becomes a Logarithmic CFT at mu = 1.
We examine the relations between observables in two- and three-dimensional quantum gravity by studying the coupling of topologically massive gravity to matter fields in non-trivial representations of the three-dimensional Lorentz group. We show that the gravitational renormalization of spin up to one-loop order in these theories reproduces the leading orders of the KPZ scaling relations for quantum Liouville theory. We demonstrate that the two-dimensional scaling dimensions can be computed from tree-level Aharonov-Bohm scattering amplitudes between the charged particles in the limit where the …
We solve the equations of topologically massive gravity with potentially non-vanishing cosmological constant for homogeneous metrics without isotropy. We only reproduce known solutions. We also discuss their homogeneous deformations, possibly with isotropy. We show that de Sitter space and hyperbolic space cannot be infinitesimally homogeneously deformed in TMG. We clarify some of their Segre-Petrov types and discuss the warped de Sitter spacetime.
We classify all stationary axi-symmetric solutions of topologically massive gravity into Einstein, Schrödinger, warped and generic solutions. We construct explicitly all local solutions in the first three sectors and present an algorithm for the numerical construction of all local solutions in the generic sector. The only input for this algorithm is the value of one constant of motion if the solution has an analytic centre, and three constants of motion otherwise. We present several examples, including soliton solutions that asymptote to warped AdS.
Making use of Achucarro-Ortiz (AO) type of dimensional reduction, we study the topologically massive gravity with a negative cosmological constant on AdS2 spacetimes. For a constant dilaton, this two-dimensional model also admits three AdS2 vacuum solutions, which are related to two AdS3 and warped AdS3 backgrounds with an identification upon uplifting three dimensions. We carry out the perturbation analysis around these backgrounds to find what is a physically propagating field. However, it turns out that there is no propagating massive mode on AdS2 background, in contrast to the Kaluza-Klein…
We extend topologically massive electrodynamics, both by adding a higher derivative action to cast the entire three-term model in Chern-Simons (CS) form, and by embedding it in an AdS background. It can then be written as the sum of two CS terms, one of which vanishes at the "chiral" point, in analogy with its gravitational topologically massive counterpart. Separately we treat pure CS electrodynamics plus Einstein gravity interacting with point sources. The gravity/vector field equations decouple; their solutions are the familiar exterior "conical" metric and vector potentials.
We study exact solutions of three-dimensional gravity with a cosmological constant and a gravitational Chern-Simons term: the theory known as topologically massive gravity. After reviewing the algebraic classification, we show that if a solution has curvature of algebraic type D, then it is biaxially squashed AdS_3. Applying the classification, we provide a comprehensive review of the literature, showing that most known solutions are locally equivalent to biaxially squashed AdS_3 or to AdS pp-waves.
The anomaly cancelation method proposed by Wilczek et al. is applied to the black holes of topologically massive gravity (TMG) and topologically massive gravito-electrodynamics (TMGE). Thus the Hawking temperature and fluxes of the ACL and ACGL black holes are found. The Hawking temperatures obtained agree with the surface gravity formula. Both black holes are rotating and this gives rise to appropriate terms in the effective U(1) gauge field of the reduced (1+1)-dimensional theory. It is found that the terms in this U(1) gauge field correspond exactly to the correct angular velocities on the …
Some classical aspects of Metric-Affine Gravity are reviewed in the context of the $F^{(n)}(R)$ type models (polynomials of degree $n$ in the Riemann tensor) and the topologically massive gravity. At the non-perturbative level, we explore the consistency of the field equations when the $F^{(n)}(R)$ models are reduced to a Riemann-Christoffel (RCh) space-time, either via a Riemann-Cartan (RC) space or via an Einstein-Weyl (EW) space. It is well known for the case $F^{(1)}(R)=R$ that any path or reduction "classes" via RC or EW, leads to the same field equations with the exception of the $F^{(n)…
We propose a set of consistent boundary conditions containing the spacelike warped black holes solutions of Topologically Massive Gravity. We prove that the corresponding asymptotic charges whose algebra consists in a Virasoro algebra and a current algebra are finite, integrable and conserved. A similar analysis is performed for the timelike warped AdS_3 spaces which contain a family of regular solitons. The energy of the boundary Virasoro excitations is positive while the current algebra leads to negative (for the spacelike warped case) and positive (for the timelike warped case) energy bound…
Recently, an extension of the topologically massive gravity (TMG) in $2+1$ dimensions, dubbed as minimal massive gravity (MMG), was found which is free of the bulk-boundary unitarity clash that inflicts the former theory and all the other known three dimensional theories. Field equations of MMG differ from those of TMG at quadratic terms in the curvature that do not come from the variation of an action depending on the metric alone. Here we show that MMG is a unique theory and there does not exist a deformation of TMG or MMG at the cubic and quartic order (and beyond) in the curvature that is …
I discuss the applicability in Weyl-invariant induced gravity and topologically massive gravity of certain formulas originally derived by Knizhnik, Polyakov, and Zamolodchikov in the context of diffeomorphism-invariant induced gravity.
We demonstrate that the warped AdS3 black hole solutions of Topologically Massive Gravity are classically stable against massive scalar field perturbations by analysing the quasinormal and bound state modes of the scalar field. In particular, it is found that although classical superradiance is present it does not give rise to superradiant instabilities. The stability is shown to persist even when the black hole is enclosed by a stationary mirror with Dirichlet boundary conditions. This is a surprising result in view of the similarity between the causal structure of the warped AdS3 black hole …
We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three-dimensional Riemann-Cartan space-times. We use the language of exterior differential forms and the properties of Majorana spinors on 3-dimensional space-times to explicitly demonstrate the local supersymmetry of the action density involved. Coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion-constraint imposed by the method of Lagrange multipliers. We compare these field equations with…
We look at the generalisation of topologically massive gravity (TMG) to higher spins, specifically spin-3. We find a special "chiral" point for the spin-three, analogous to the spin-two example, which actually coincides with the usual spin-two chiral point. But in contrast to usual TMG, there is the presence of a non-trivial trace and its logarithmic partner at the chiral point. The trace modes carry energy opposite in sign to the traceless modes. The logarithmic partner of the traceless mode carries negative energy indicating an instability at the chiral point. We make several comments on the…
A Lagrangian formulation describing the electromagnetic interaction - mediated by topologically massive vector bosons - between charged, spin-(1/2) fermions with an abelian magnetic monopole in a curved spacetime with non-minimal coupling and torsion potential is presented. The covariant field equations are obtained. The issue of coexistence of massive photons and magnetic monopoles is addressed in the present framework. It is found that despite the topological nature of photon mass generation in curved spacetime with isotropic dilaton field, the classical field theory describing the nonrelati…
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 o…
In this paper, we investigate relativistic quantum dynamics of spin- $0$ massive charged particle subject to a homogeneous magnetic field in the Gödel-type space-time with potentials. We solve the Klein-Gordon equation subject to a homogeneous magnetic field in a topologically trivial flat class of Gödel-type space-time in the presence of a Cornell-type scalar and Coulomb-type vector potentials and analyze the effects on the energy eigenvalues and eigenfunctions.
Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic relationship between two a priori independent boundary data: the boundary energy-momentum tensor and the boundary Cotton tensor. This relationship, which can be viewed as resulting from a topological mass term for gravity boundary dynamics, survives under the Lorentzian signature and provides a tool for generating exact bulk Einstein spaces carrying, among others, nut charge. In turn, the holographic analysis exhibits per…
We consider renormalizability of topologically massive gravity in three space-time dimensions. With a usual parametrization of the metric tensor, we establish the statement that topologically massive gravity is in fact renormalizable. In this proof, we make use of not only a recently found, new infrared regularization method of scalar mode but also a covariant ultraviolet regulator with a specific combination of higher derivative terms which is motivated by the new massive gravity in three dimensions.
We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter $μ$ ($μ\neq0$). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower fall-off than the one relevant for General Relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generat…
We study the classical solutions of three dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first order formulation. The action of higher spin TMG has been proposed in arXiv:1110.5113 to be of a Chern-Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS$_3$ gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair, and find that the nonvanish…
We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtai…
An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the unitarity of both topologically massive higher-derivative electromagnetism and topologically massive higher-derivative gravity. The novel and amazing features of these effective field models are also discussed.
The superfield equations of massive IIA supergravity, in the form of constraints on the superspace geometry, are shown to be implied by $κ$-symmetry of the topologically massive D-2-brane.
We consider three dimensional gravity with a positive cosmological constant and non- zero gravitational Chern-Simons term. This theory has inflating de Sitter solutions and local metric degrees of freedom. The Euclidean signature partition function of the theory is evaluated including both perturbative and non-perturbative corrections. The perturbative one-loop correction is computed using heat kernel techniques. The non- perturbative corrections come from gravitational instantons with non-trivial topology which can be enumerated explicitly. We compute the sum over an infinite class of ge- ome…
We investigate the topologically new massive gravity in three dimensions. It turns out that a single massive mode is propagating in the flat spacetime, comparing to the conformal Chern-Simons gravity which has no physically propagating degrees of freedom. Also we discuss the realization of the BMS/GCA correspondence.
We consider the conformally-invariant coupling of topologically massive gravity to a dynamical massless scalar field theory on a three-manifold with boundary. We show that, in the phase of spontaneously broken Lorentz and Weyl symmetries, this theory induces the target space zero mode of the vertex operator for the string dilaton field on the boundary of the three-dimensional manifold. By a further coupling to topologically massive gauge fields in the bulk, we demonstrate directly from the three-dimensional theory that this dilaton field transforms in the expected way under duality transformat…
Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological constant are considered in the case of spacelike stretched warping, where black holes have been shown to exist. We provide a set of asymptotic conditions that accommodate solutions in which the local degree of freedom (the "massive graviton") is switched on. An exact solution with this property is explicitly exhibited and possesses a slower fall-off than the warped AdS black hole. The boundary conditions are invariant under the semidirect product of the Virasoro algebra with a u(1) current algebra.…
The addition of a topologically massive term to an admittedly non-unitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its non-unitarity. What about the enlargement of avowedly unitary massive models by way of a topologically massive term? The electromagnetic models remain unitary after the topological augmentation but, surprisingly enough, the gravitational ones have their unitarity spoiled. Here we analyze these issues and present the explanation why unitary massive gravitational models, unlike unitary massive electromagnetic ones, ca…
We consider cosmological topologically massive gravity at the chiral point with positive sign of the Einstein-Hilbert term. We demonstrate the presence of a negative energy bulk mode that grows linearly in time. Unless there are physical reasons to discard this mode, this theory is unstable. To address this issue we prove that the mode is not pure gauge and that its negative energy is time-independent and finite. The isometry generators L_0 and \bar{L}_0 have non-unitary matrix representations like in logarithmic CFT. While the new mode obeys boundary conditions that are slightly weaker than t…
We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. We find that ν, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on ν, and for any positive νthere exist both a trivial and a nontrivial fixed point.
