Critical points of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>-dimensional extended gravities

Deser, S.; Liu, Haishan; Lü, H.; Pope, C.N.; Şişman, Tahsin Çağrı; Tekin, Bayram

doi:10.1103/physrevd.83.061502

Cited by 142 publications

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“…Then, taking the metric to be in the Kundt subclass of type-N spacetimes we show that AdS-plane wave [7,8] and AdS-spherical wave [9] solutions of the quadratic gravity theory are also the solutions of the f R µν ρσ theory. Log terms arising in the solutions of the quadratic gravity exist also in some f R µν ρσ theories corresponding to the generalizations of critical gravity [10,11]. As an application of our result, we show that any type-N Einstein space R µν = R D g µν solve the field equations of the Lanczos-Lovelock theory.…”

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confidence: 74%

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

et al. 2013

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We show that the recently found AdS-plane and AdS-spherical wave solutions of quadratic curvature gravity also solve the most general higher derivative theory in D-dimensions. More generally, we show that the field equations of such theories reduce to an equation linear in the Ricci tensor for Kerr-Schild spacetimes having type-N Weyl and traceless Ricci tensors. PACS numbers:There is a vast literature on the exact solutions of fourdimensional Einstein's gravity. But, as more powers of curvature are added, or computed in a microscopic theory such as string theory, to get a better UV behaved theory, the field equations become highly nontrivial and so solutions are not easy to find. In fact, only a few classes of solutions are known: For example, see [1][2][3][4] for solutions in low energy string theory. AdS 5 × S 5 , which played a major role in AdS/CFT, is also expected to be an exact solution of string theory [5]. In this work, we present new asymptotically AdS solutions, which are AdS-plane and AdS-spherical waves, to D-dimensional generic gravity theories based on the Riemann tensor and its arbitrary number of covariant derivatives which are in some sense natural geometric extensions of Einstein's gravity. Certain low energy string theory actions constitute a subclass of this theory once all the non-gravitational fields are turned off [6]. Asymptotically AdS solutions in higher derivative theories are relevant in the context of generic gravity/gauge theory dualities and holography. Here, we shall provide such solutions.Using a theorem given in [4], we first prove that any spacetime with type-N Weyl and traceless Ricci tensors, where the metric is the Kerr-Schild form, the field equations of the most general higher derivative theory reduce to a linear equation for the traceless Ricci tensor. These spacetimes have constant scalar invariants. Furthermore, using the the type-N property of the traceless Ricci tensor in these field equations, we obtain a linear partial differential equation for the metric function V of order 2N in the AdS background, where N is related to the number of covariant derivatives in the action of the theory. This result implies that the AdS-wave metrics are universal in the sense defined in [4].As a special case, the field equations of the theory * Electronic address: gurses@fen.bilkent.edu.tr † Electronic address: sigbjorn.hervik@uis.no ‡ Electronic address: tahsin.c.sisman@gmail.com § Electronic address: btekin@metu.edu.tr which depends on the contractions of the Riemann tensor but not on its derivatives, f R µν ρσ theory, arealso highly cumbersome, but using our general result for type-N spacetimes under certain assumptions they reduce to those of the quadratic gravity. Then, taking the metric to be in the Kundt subclass of type-N spacetimes we show that AdS-plane wave [7,8] and AdS-spherical wave [9] solutions of the quadratic gravity theory are also the solutions of the f R µν ρσ theory. Log terms arising in the solutions of the quadratic gravity exist also in some f R µν ρσ theori...

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confidence: 74%

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

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“…The correspondence between logarithmic CFTs with c = 0 and higher derivative gravity theories is nicely reviewed in [47], with a focus on the three-dimensional bulk theories. Here we merely point out a simple example, that of "new massive gravity" in d + 1 dimensions [74][75][76][77]. The action is…”

Section: Spin-2mentioning

confidence: 99%

“…The irreducible representations appearing in the OPE of the field φ a with itself were worked out a long time ago [91], with a more detailed analysis appearing in [92,93]. We can schematically write the OPE 13 77) with the projector P ab being defined by…”

Section: Jhep10(2017)201mentioning

confidence: 99%

The ABC (in any D) of logarithmic CFT

Hogervorst

Paulos

Vichi

2017

J. High Energ. Phys.

103

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Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is modelindependent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.

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“…Ostrogradsky procedure [22] leads to the following bulk excitation energies (up to positive multiplicative constants) that satisfy the field equations for the massless modes…”

Section: Solutions Of the Linearized Equationsmentioning

confidence: 99%

Bulk and boundary unitary gravity in 3D:MMG2

Tekin¹

2015

Phys. Rev. D

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We construct a massive spin-2 theory in 2+1 dimensions that is immune to the bulk-boundary unitarity conflict in anti-de Sitter space and hence amenable to holography. The theory is an extension of Topologically Massive Gravity, just like the recently found Minimal Massive Gravity (MMG), but it has two massive helicity modes instead of a single one. The theory admits all the solutions of TMG with a redefined topological parameter. We calculate the Shapiro time-delay and show that flat-space (local) causality is not violated. We show that there is an interesting relation between the theory we present here (which we call MMG2), MMG and the earlier New Massive Gravity (NMG): Namely, field equations of these theories are non-trivially related. We study the bulk excitations and boundary charges of the conformal field theory that could be dual to gravity. We also find the chiral gravity limit for which one of the massive modes becomes massless. The virtue of the model is that one does not have to go to the chiral limit to achieve unitarity in the bulk and on the boundary and the log-terms that appear in the chiral limit and cause instability do not exist in the generic theory.PACS numbers: I. INTRODUCTIONGravity in 2+1 dimensions has a counterintuitive richness: On the one side, naive counting from the metric leads to the conclusion that once gauge invariance (diffeomorphism invariance) is taken into account, no local propagating degrees of freedom (gravitons or gravity waves) exist, as in the case of Einstein's gravity. On the other hand, modifications of the theory, such as with higher powers of curvature introduce non-trivial local dynamics along with, usually, massive gravitons. Therefore, while it is very hard to get non-linear, unitary, ghostfree massive gravity in 3+1 dimensions with 5 degrees of freedom, it is embarrassingly easy to get massive gravity with 2 degrees of freedom in one lower dimensions. By now there there are several 3D models : Topologically Massive Gravity (TMG),[1], New Massive Gravity (NMG) [2] and the recent Minimal Massive Gravity (MMG) [3,4]. TMG is a parity-violating theory with a single spin-2 degree of freedom, NMG has a massive spin-2 excitation with both helicities, while MMG has a single massive parity-violating spin-2 excitation (same as TMG) but free of the bulk-boundary unitarity conflict in anti-de Sitter(AdS)spacetime that inflicts NMG and TMG. Ultimately, of course, research in 3D gravity aims at understanding or building "quantum gravity" in the physically relevant spacetime. For this purpose, obtaining a unitary, nontrivial gravity theory that has a welldefined unitary conformal field theory on the boundary is an important step. For example, NMG which has 2 massive bulk excitations just like General Relativity in 4D (with a massless graviton) does not have a unitary * Electronic address: btekin@metu.edu.tr conformal field theory (CFT) on the boundary. [Elaborate extensions of NMG could not resolve the issue [5,6].] Hence MMG stands alone as a curious non-trivial case of a 3...

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Critical points ofD-dimensional extended gravities

Cited by 142 publications

References 18 publications

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

Anti–de Sitter–Wave Solutions of Higher Derivative Theories

The ABC (in any D) of logarithmic CFT

Bulk and boundary unitary gravity in 3D:MMG2

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