In this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the continuum. We will argue, in particular, that in three spacetime dimensions the discrete spectra for the geometric boundary observables that we find in loop quantum gravity can be understood from the quantisation of a conformal boundary field theory in the continuum without ever introducing spin networks or triangulations of space. At a technical level, the starting point is the Hamiltonian formalism for general relativity in regions with boundaries at finite distance. At these finite boundaries, we choose specific conformal boundary conditions (the boundary is a minimal surface) that are derived from a boundary field theory for an SU(2) boundary spinor, which is minimally coupled to the spin connection in the bulk. The resulting boundary equations of motion define a conformal field theory with vanishing central charge. We will quantise this boundary field theory and show that the length of a one-dimensional cross section of the boundary has a discrete spectrum. In addition, we will introduce a new class of coherent states, study the quasi-local observables that generate the quasi-local Virasoro algebra and discuss some strategies to evaluate the partition function of the theory.
We extend Maldacena's argument, namely, obtaining Einstein gravity from Conformal Gravity, to six dimensional manifolds. The proof relies on a particular combination of conformal (and topological) invariants, which makes manifest the fact that 6D Conformal Gravity admits an Einstein sector. Then, by taking generalized Neumann boundary conditions, the Conformal Gravity action reduces to the renormalized Einstein-AdS action. These restrictions are implied by the vanishing of the traceless Ricci tensor, which is the defining property of any Einstein spacetime. The equivalence between Conformal an…
We consider holography of two pp-wave metrics in conformal gravity, their one point functions, and asymptotic symmetries. One of the metrics is a generalization of the standard pp-waves in Einstein gravity to conformal gravity. The holography of this metric shows that within conformal gravity one can have realised solution which has non-vanishing partially massless response (PMR) tensor even for vanishing subleading term in the Fefferman-Graham expansion (i.e. Neumann boundary conditions), and vice-versa.
We provide a new derivation of the Hawking mass and Willmore energy functionals for asymptotically AdS spacetimes, by embedding Einstein-AdS gravity in Conformal Gravity. By construction, the evaluation of the four-dimensional Conformal Gravity action in a manifold with a conical defect produces a codimension-2 conformal invariant functional $L_Σ$. The energy functionals are then particular cases of $L_Σ$ for Einstein-AdS and pure AdS ambient spaces, respectively. The bulk action is finite for AdS asymptotics and both Hawking mass and Willmore energy are finite as well. The result suggests a g…
We present a new class of solutions for static spherically symmetric wormhole spacetimes in conformal gravity and outline a detailed method for their construction. As an explicit example, we construct a class of traversable and non-traversable wormholes that are locally conformal to Schwarzschild-(anti) de Sitter spacetimes. These wormhole spacetimes are exact vacuum solutions in, but not being limited to, Weyl gravity and conformal scalar-tensor theories. Importantly, the method implies that every conformal theory of gravity with static spherically symmetric solutions will trivially contain w…
We study the gravity action built from two gauge fields corresponding to the generators of the conformal group. Starting with the action from which one can obtain Einstein gravity and conformal gravity upon imposing suitable constraints, we keep two independent gauge fields and integrate out the field corresponding to the generator of Lorentz transformations. We identify the two gauge fields with two vierbeins and perturb them around an Anti--de Sitter space. This gives the linearized equations that differ from both, Einstein gravity and conformal gravity linearized equations. We also study th…
The solutions of the Einstein equation are a subset of the solutions of conformal (Weyl) gravity, but the difference from the action means that the black hole thermodynamics of the two gravity theories would be different. In this paper we explore the thermodynamic phase structure for the conformal gravity in the four-dimensional AdS space-time. Special emphasis is put on the dependence on the parameter $c_1$ in the linear-$r$ term in the metric. The thermodynamic phase structure of the conformal gravity is very rich, including two branches of equations of states, negative thermodynamic volume,…
We investigate the black holes in the new massive conformal gravity which is not invariant under conformal transformations because of the presence of the Einstein-Hilbert term. First, we show that the small Schwarzschild black hole is unstable against the $s$-mode of linearized Ricci tensor by solving the Lichnerowicz-Ricci tensor equation. This instability induces the appearance of the non-BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole that has both Ricci tensor and conformal scalar hair.
Noncritical Conformal Gravity and Four-Dimensional Liouville Theory
National Taiwan University（台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（大阪公立大学南阳一郎理论与实验物理研究所（NITEP））；Institute of Fundamental Physics and Quantum Technology, Department of Physics, School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院物理学与量子技术基础物理研究所）
The Janis-Newman-Winicour metric is a solution of Einstein's gravity minimally coupled to a real massless scalar field. The $γ$-metric is instead a vacuum solution of Einstein's gravity. These spacetimes have no horizon and possess a naked singularity at a finite value of the radial coordinate, where curvature invariants diverge and the spacetimes are geodetically incomplete. In this paper, we reconsider these solutions in the framework of conformal gravity and we show that it is possible to solve the spacetime singularities with a suitable choice of the conformal factor. Now curvature invaria…
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic completion of the spacetime when it is probed by massive, massless, and conformally coupled particles. As a universal feature of the regular metric, nothing can reach the singularity located in t=0 in a finite amount of proper time (for massive particles and conformally coupled particles) or for finite values of the affine parameter (for massless particles).
We examine the question of scale vs. conformal invariance for the linearized Einstein-Hilbert action, which describes the IR fixed point of quantum gravity. In $D = 4$, although the action is not conformally invariant in the usual sense, we explicitly show that the theory is a conformal field theory at the level of correlation functions. In higher dimensions, we show that the theory is scale but not conformally invariant, but can be embedded into a larger non-unitary conformal field theory, analogous to what has been found for Maxwell theory in $D>4$. We give evidence that similar statements a…
In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$\ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$\ and $c_{2}$ are acceptable.
On the Renormalization in Conformal Quantum Gravity
Joint Institute for Nuclear Research（俄罗斯联合核研究所）；Tomsk State Pedagogical University（托木斯克国立师范学院）；Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；Universidade Federal de Juiz de Fora（儒塞夫联邦大学）
The presence of an unstable massive spin-2 ghost state in the renormalizable theory of massive conformal gravity leads to a pair of complex poles appearing in the first sheet of the energy plane. Here we show that the positions of these poles are gauge dependent, which makes the theory unitary.
