Class Of Gravity Theories Research Articles

Geometric encoding of renormalization group β -functions in an emergent holographic dual description

First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG $\beta-$functions of coupling functions and RG flow equation of the order-parameter field appear in the resulting effective action explicitly through the extra dimensional space. Second, we consider an effective dual holographic description derived recently, where the classical gravity theory of the large $N$ limit takes into account quantum corrections in the all-loop order. This non-perturbative nature turns out to originate from an intertwined renormalization structure between both RG flow equations of coupling functions and order-parameter fields in the emergent extra-dimensional space, where the IR boundary condition of the order-parameter field gives rise to a mean-field equation with fully renormalized interaction coefficients. Third, comparing the RG-reformulated effective field theory with this effective dual holographic description, we obtain term-by-term matching conditions in the level of an effective action. As a result, we express all RG coefficients of fields and interaction vertices in terms of the metric tensor of the dual holographic theory. Through this metric reformulation for the RG analysis, we propose a prescription on how to find RG $\beta-$functions of interaction coefficients in a non-perturbative way beyond the perturbative RG analysis. In particular, we claim that the present prescription of the RG flow generalizes the holographic RG flow of the holographic duality conjecture towards the absence of conformal symmetry, where the emergent holographic dual effective field theory has been derived from the first principle, thus being applicable even away from quantum criticality.

De Sitter field equations from quadratic curvature gravity: A group theoretical approach

In this paper, the linearized field equations related to the quadratic curvature gravity theory have been obtained in the four-dimensional de Sitter (dS) space–time. The massless spin-2 field equations have been written in terms of the Casimir operators of dS group making use of the ambient space notations. By imposing some simple constraints, arisen from group theoretical interpretation of the field equations, a new four-dimensional Gauss–Bonnet (GB-)like action has been introduced with the related field equations transforming according to the unitary irreducible representations (UIRs) of dS group. Since, the field equations transform according to the UIRs of dS group, the GB-like action, we just obtained, is expected to be a successful model of modified gravity. For more clarity, the gauge invariant field equations have been solved in terms of a gauge-fixing parameter [Formula: see text]. It has been shown that the solution can be written as the multiplication of a symmetric rank-2 polarization tensor and a massless minimally coupled scalar field on dS space. The Krein–Gupta–Bleuler quantization method has been utilized and the covariant two-point function has been calculated in terms of the massless minimally coupled scalar two-point function, using the ambient space notations. It has been written in terms of dS intrinsic coordinates from the ambient space counterpart. The two-point functions are dS invariant and free of any theoretical problems. It means that the proposed model is a successful model of modified gravity and it can produce significant results in the contexts of classical theory of gravity and quantum gravity toy models.

Dynamics of DiskMass Survey galaxies in refracted gravity

We aim to verify whether refracted gravity (RG) is capable of describing the dynamics of disk galaxies without resorting to the presence of dark matter. RG is a classical theory of gravity in which the standard Poisson equation is modified with the introduction of the gravitational permittivity, which is a universal monotonic function of the local mass density. We used the rotation curves and the radial profiles of the stellar velocity dispersion perpendicular to the galactic disks of 30 disk galaxies from the DiskMass Survey (DMS) to determine the gravitational permittivity. RG describes the rotation curves and the vertical velocity dispersions by requiring galaxy mass-to-light ratios that are in agreement with stellar population synthesis models, and disk thicknesses that are in agreement with observations, once observational biases are taken into account. Our results rely on setting the three free parameters of the gravitational permittivity for each individual galaxy. However, we show that the differences of these parameters from galaxy to galaxy can, in principle, be ascribed to statistical fluctuations. We adopted an approximate procedure to estimate a single set of parameters that may properly describe the kinematics of the entire sample and suggest that the gravitational permittivity is indeed a universal function. Finally, we showed that the RG models of the individual rotation curves can only partly describe the radial acceleration relation (RAR) between the observed centripetal acceleration derived from the rotation curve and the Newtonian gravitational acceleration originating from the baryonic mass distribution. Evidently, the RG models underestimate the observed accelerations by 0.1 to 0.3 dex at low Newtonian accelerations. An additional problem that ought to be considered is the strong correlation, at much more than 5σ, between the residuals of the RAR models and three radially-dependent properties of the galaxies, whereas the DMS data show a considerably less significant correlation, at more than 4σ, for only two of these quantities. These correlations might be the source of the non-null intrinsic scatter of the RG models: this non-null scatter is at odds with the observed intrinsic scatter of other galaxy samples different from DMS, which is consistent with zero. Further investigations are required to assess whether these discrepancies in the RAR originate from the DMS sample, which might not be ideal for deriving the RAR, or whether they are genuine failures of RG.

Surface charges toolkit for gravity

These notes provide a detailed catalog of surface charge formulas for different classes of gravity theories. The present catalog reviews and extends the existing literature on the topic. Part of the focus is on reviewing the method to compute quasi-local surface charges for gauge theories in order to clarify conceptual issues and their range of applicability. Many surface charge formulas for gravity theories are expressed in metric, tetrads-connection, Chern–Simons connection, and even BF variables. For most of them, the language of differential forms is exploited and contrasted with the more popular metric components language. The gravity theory is coupled with matter fields as scalar, Maxwell, Skyrme, Yang–Mills, and spinors. Furthermore, three examples with ready-to-download notebook codes, show the method in full action. Several new results are highlighted through the notes.

New class of generalized coupling theories

We propose a new class of gravity theories which are characterized by a nontrivial coupling between the gravitational metric and matter mediated by an auxiliary rank-2 tensor. The actions generating the field equations are constructed so that these theories are equivalent to general relativity in a vacuum, and only differ from general relativity theory within a matter distribution. We analyze in detail one of the simplest realizations of these generalized coupling theories. We show that in this case the propagation speed of gravitational radiation in matter is different from its value in vacuum and that this can be used to weakly constrain the (single) additional parameter of the theory. An analysis of the evolution of homogeneous and isotropic spacetimes in the same framework shows that there exist cosmic histories with both an inflationary phase and a dark era characterized by a different expansion rate.

Observations of the Sun’s Dragging Forces

The classical theory of gravity, developed by Isaac Newton, predicts that the gravitational force between two masses is always colinear with the direction defined by the center of mass of both bodies. Some work done in the last 60 years has shown experimental evidence that the reality may be somehow more complex. That complexity was confirmed by the author of this paper and he goes farther announcing that the Sun is emitting particles with 44 m spatial periodicity that creates isotropic gravitational effects. Those effects are identical to the ones produced by dragging forces according to the General Theory of Relativity under the Kerr’s Metric. The purpose of this paper is to introduce experimental evidence confirming the author’s predictions that the Moon can modify the dragging force coming from the Sun’s core.

Proposal for a New Quantum Theory of Gravity III: Equations for Quantum Gravity, and the Origin of Spontaneous Localisation

Abstract We present a new, falsifiable quantum theory of gravity, which we name non-commutative matter-gravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the concept of an atom of space-time-matter (STM), which is described by the spectral action in non-commutative geometry, corresponding to a classical theory of gravity. We used the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derived the spectral equation of motion for the gravity part of the STM atom, which turns out to be the Dirac equation on a non-commutative space. In the present work, we propose how to include the matter (fermionic) part and give a simple action principle for the STM atom. This leads to the equations for a quantum theory of gravity, and also to an explanation for the origin of spontaneous localisation from quantum gravity. We use spontaneous localisation to arrive at the action for classical general relativity (including matter source) from the action for STM atoms.

Proposal for a New Quantum Theory of Gravity II

Abstract In the first article of this series, we have introduced the concept of an atom of space-time-matter (STM), which is described by the spectral action of noncommutative geometry, corresponding to a classical theory of gravity. In the present work, we use the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derive the spectral equation of motion for the STM atom, which turns out to be the Dirac equation on a noncommutative space.

Proposal for a New Quantum Theory of Gravity

Abstract We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space–time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity are both seen as emergent phenomena, resulting from coarse graining of the underlying noncommutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space–time–matter, and indeed entanglement appears to be more fundamental than quantum theory or space–time. We also comment on possible implications for black hole entropy and evaporation and for cosmology. We list the intermediate mathematical analysis that remains to be done to complete this programme.

Hamilton–Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity

The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous deDonder–Weyl variational formulation (2015–2019). In such a setting, the canonical variables defining the canonical state acquire different tensorial orders, with the momentum conjugate to the field variable g μ ν being realized by the third-order 4-tensor Π μ ν α . It is shown that this generates a corresponding Hamilton–Jacobi theory in which the Hamilton principal function is a 4-tensor S α . However, in order to express the Hamilton equations as evolution equations and apply standard quantization methods, the canonical variables must have the same tensorial dimension. This can be achieved by projection of the canonical momentum field along prescribed tensorial directions associated with geodesic trajectories defined with respect to the background space-time for either classical test particles or raylights. It is proved that this permits to recover a Hamilton principal function in the appropriate form of 4-scalar type. The corresponding Hamilton–Jacobi wave theory is studied and implications for the manifestly-covariant quantum gravity theory are discussed. This concerns in particular the possibility of achieving at quantum level physical solutions describing massive or massless quanta of the gravitational field.

The fate of black hole horizons in semiclassical gravity

The presence of a horizon is the principal marker for black holes as they appear in the classical theory of gravity. In General Relativity (GR), horizons have several defining properties. First, there exists a static spherically symmetric solution to vacuum Einstein equations which possesses a horizon defined as a null-surface on which the time-like Killing vector becomes null. Second, in GR, a co-dimension two sphere of minimal area is necessarily a horizon. On a quantum level, the classical gravitational action is supplemented by the quantum effective action obtained by integrating out the quantum fields propagating on a classical background. In this note we consider the case when the quantum fields are conformal and perform a certain non-perturbative analysis of the semiclassical equations obtained by varying the complete gravitational action. We show that, for these equations, both of the above aspects do not hold. More precisely, we prove that i) a static spherically symmetric metric that would describe a horizon with a finite Hawking temperature is, generically, not a solution; ii) a minimal 2-sphere is not a horizon but a tiny throat of a wormhole. We find certain bounds on the norm of the Killing vector at the throat and show that it is, while non-zero, an exponentially small function of the Bekenstein–Hawking (BH) entropy of the classical black hole. We also find that the possible temperature of the semiclassical geometry is exponentially small for large black holes. These findings suggest that a black hole in the classical theory can be viewed as a certain (singular) limit of the semiclassical wormhole geometry. We discuss the possible implications of our results.

Measurable signatures of quantum mechanics in a classical spacetime

We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schroedinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator's center of mass wavefunction differ from the predictions of standard quantum mechanics. This difference is largest for low-frequency oscillators, and for materials, such as Tungsten or Osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum's dynamics. Due to the non-linearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wavefunction collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light's phase fluctuations' spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology.

Hamiltonian approach to GR \u2013 Part 1: covariant theory of classical gravity

A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton–Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor widehat{g}(r)equiv { widehat{g}_{mu nu }(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields xequiv { g,pi } obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton–Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

Induction equations for fundamental fields and dark matter

The paper outlines some aspects of the theory of gravity and electromagnetism based on a topology-geometric interpretation of matter and its properties as manifestations of a non-Euclidean geometry of the physical hypersurface of dimension 3 embedded in a Euclidean space of dimension 4. We derive the basic equations of the theory, leading to equations similar to those of the classical theory of gravity and electromagnetism as well as those of quantum theory. It is shown that in this theory the observed effect of a hidden mass, or dark matter, is explained in a natural way by effects of the geometry of the physical hypersurface.

Illustrated study of the semiholographic nonperturbative framework

Semi-holography has been proposed as an effective nonperturbative framework which can combine perturbative and nonperturbative effects consistently for theories like QCD. It is postulated that the strongly coupled nonperturbative sector has a holographic dual in the form of a classical gravity theory in the large N limit, and the perturbative fields determine the gravitational boundary conditions. In this work, we pursue a fundamental derivation of this framework particularly showing how perturbative physics by itself can determine the holographic dual of the infrared, and also the interactions between the perturbative and the holographic sectors. We firstly demonstrate that the interactions between the two sectors can be constrained through the existence of a conserved local energy-momentum tensor for the full system up to hard-soft coupling constants. As an illustration, we set up a bi-holographic toy theory where both the UV and IR sectors are strongly coupled and holographic with distinct classical gravity duals. In this construction, the requirement that an appropriate gluing can cure the singularities (geodetic incompletenesses) of the respective geometries leads us to determine the parameters of the IR theory and the hard-soft couplings in terms of those of the UV theory. The high energy scale behaviour of the hard-soft couplings is state-independent but their runnings turn out to be state-dependent. We discuss how our approach can be adapted to the construction of the semi-holographic framework for QCD.

Holography as a highly efficient renormalization group flow. I. Rephrasing gravity

We investigate how the holographic correspondence can be reformulated as a generalisation of Wilsonian RG flow in a strongly interacting large $N$ quantum field theory. We firstly define a \textit{highly efficient RG flow} as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale -- to achieve this it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single trace operators. These redefinitions also absorb the contributions of the multi-trace operators to these effective Ward identities. Thus the background metric and external sources become effectively dynamical reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is \textit{unique} provided the endpoint can be transformed to a non-relativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow, and obtain the dual classical gravity theory.

Holography as a highly efficient renormalization group flow. II. An explicit construction

We complete the reformulation of the holographic correspondence as a \emph{highly efficient RG flow} that can also determine the UV data in the field theory in the strong coupling and large $N$ limit. We introduce a special way to define operators at any given scale in terms of appropriate coarse-grained collective variables, without requiring the use of the elementary fields. The Wilsonian construction is generalised by promoting the cut-off to a functional of these collective variables. We impose three criteria to determine the coarse-graining. The first criterion is that the effective Ward identities for local conservation of energy, momentum, etc. should preserve their standard forms, but in new scale-dependent background metric and sources which are functionals of the effective single trace operators. The second criterion is that the scale-evolution equations of the operators in the actual background metric should be state-independent, implying that the collective variables should not explicitly appear in them. The final criterion is that the endpoint of the scale-evolution of the RG flow can be transformed to a fixed point corresponding to familiar non-relativistic equations with a finite number of parameters, such as incompressible non-relativistic Navier-Stokes, under a certain universal rescaling of the scale and of the time coordinate. Using previous work, we explicitly show that in the hydrodynamic limit each such highly efficient RG flow reproduces a unique classical gravity theory with precise UV data that satisfy our IR criterion. We obtain the explicit coarse-graining which reproduces Einstein's equations. In a simple example, we are also able to compute the beta function. Finally, we show how our construction can be interpolated with the traditional Wilsonian RG flow at a suitable scale, and can be used to develop new non-perturbative frameworks for QCD-like theories.

Generalized Yang-Mills theory and gravity

We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories in general include a graviton, a dilaton and a rank-2 antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via BCJ duality can be made more manifest in this formulation.

Toward black hole entropy in shape dynamics

Shape dynamics is a classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes spatial diffeomorphism invariance and spatial Weyl invariance as the fundamental gauge symmetries associated with the gravitational field. Since the area of the event horizon of a black hole transforms under a generic spatial Weyl transformation, there has been some doubt that one can speak sensibly about the thermodynamics of black holes in shape dynamics. The purpose of this paper is to show that by treating the event horizon of a black hole as an interior boundary, one can recover familiar notions of black hole thermodynamics in shape dynamics and define a gauge invariant entropy that agrees with general relativity.

On monopole operators in supersymmetric Chern-Simons-matter theories

We discuss monopole operators in U(N c ) Chern-Simons-matter theories in three space-time dimensions. We mention an apparent problem in the matching of such operators in dualities between non-supersymmetric theories, and suggest a possible resolution. A similar apparent problem exists in the mapping of chiral monopole operators in theories with $$ \mathcal{N} $$ = 2 supersymmetry. We show that in many theories the lowest naive chiral monopole operator is actually not chiral, and we find the lowest monopole operator that is actually chiral in these theories. It turns out that there are several different forms of this operator, depending on the number of colors, the number of flavours, and the Chern-Simons level. Since we use the supersymmetric index to find the lowest chiral monopoles, our results for these monopoles are guaranteed to be invariant under the dualities in supersymmetric theories. The theories we discuss are believed to be dual in the ’t Hooft large N c limit to classical high-spin gravity theories. We argue that these theories (supersymmetric or not) should not have classical solutions charged under the U(1) gauge field in the high-spin multiplet.