Symmetries Of Gravity Research Articles

A note on Weyl gauge symmetry in gravity

Abstract A scale invariant theory of gravity, containing at most two derivatives, requires, in addition to the Riemannian metric, a scalar field and (or) a gauge field. The gauge field is usually used to construct the affine connection of Weyl geometry. In this note, we incorporate both the gauge field and the scalar field to build a generalised scale invariant Weyl affine connection. The Ricci tensor and the Ricci scalar made out of this generalised Weyl affine connection contain, naturally, kinetic terms for the scalar field and the gauge field. This provides a geometric interpretation for these terms. It is also shown that scale invariance in the presence of a cosmological constant and mass terms is not completely lost. It becomes a duality transformation relating various fields.

Power spectra and circular polarization of primordial gravitational waves with parity and Lorentz violations

The violations of parity and Lorentz symmetries in gravity can change the propagating properties of gravitational waves (GWs) in the cosmological background, which can arise from a large number of parity- and Lorentz-violating theories. In this paper, through a systematic parametrization for characterizing possible derivations from the standard GW propagation in general relativity, we study both the parity- and Lorentz-violating effects on the power spectra and the polarization of the primordial gravitational waves (PGWs) during the slow-roll inflation. To this end, we calculate explicitly the power spectrum and the corresponding circular polarization of the PGWs analytically by using the uniform asymptotic approximation. It is shown that the new contributions to power spectra contain two parts, one from the parity-violating terms and the other from the Lorentz-violating terms. While the Lorentz-violating terms can only affect the overall amplitudes of PGWs, the parity-violating terms induce nonzero circular polarization of PGWs, i.e., the left-hand and right-hand polarization modes of GWs have different amplitudes.

Yang–Mills–Stueckelberg theories, framing and local breaking of symmetries

We consider Yang–Mills theory with a compact structure group [Formula: see text] on a Lorentzian 4-manifold [Formula: see text] such that gauge transformations become identity on a submanifold [Formula: see text] of [Formula: see text] (framing over [Formula: see text]). The space [Formula: see text] is not necessarily a boundary of [Formula: see text] and can have dimension [Formula: see text]. Framing of gauge bundles over [Formula: see text] demands introduction of a [Formula: see text]-valued function [Formula: see text] with support on [Formula: see text] and modification of Yang–Mills equations along [Formula: see text]. The fields [Formula: see text] parametrize non-equivalent flat connections mapped into each other by a dynamical group [Formula: see text] changing gauge frames over [Formula: see text]. It is shown that the charged condensate [Formula: see text] is the Stueckelberg field generating an effective mass of gluons in the domain [Formula: see text] of space [Formula: see text] and keeping them massless outside [Formula: see text]. We argue that the local Stueckelberg field [Formula: see text] can be responsible for color confinement. We also briefly discuss local breaking of symmetries in gravity. It is shown that framing of the tangent bundle over a subspace of spacetime makes gravitons massive in this subspace.

BMS symmetry in gravity: Front form versus instant form

In general relativity, the allowed set of diffeomorphisms or gauge transformations at asymptotic infinity forms the BMS group, an infinite-dimensional extension of the Poincaré group. We focus on the structure of the BMS group in two distinct forms of Hamiltonian dynamics — the instant and front forms. Both similarities and differences in these two forms are examined while emphasizing the role of noncovariant approaches to symmetries in gravity.

Additional Solar System Gravitational Anomalies

This article is motivated by uncertainty in experimental determinations of the gravitational constant, G, and numerous anomalies of up to 0.5 percent in Newtonian gravitational force on bodies within the solar system. The analysis sheds new light through six natural experiments within the solar system, which draw on published reports and astrophysical databases, and involve laboratory determinations of G, orbital dynamics of the planets and the moons of Earth and Mars, and non-gravitational acceleration (NGA) of ‘Oumuamua and comets. In each case, values are known for all variables in Newton’s Law F=G·M·mR2, except for the gravitational constant, G. Analyses determine the gravitational constant’s observed value, G^, which—across the six settings—varies with the mass of the smaller, moving body, m, so that G^=G×0.998+0.00016×lnm. While further work is required, this examination shows a scale-related Newtonian gravity effect at scales from benchtop to Solar System, which contributes to the understanding of symmetry in gravity and has possible implications for Newton’s Laws, dark matter, and formation of structure in the universe.

Asymptotic symmetries and the subleading soft graviton theorem in higher dimensions

We investigate the relation between the subleading soft graviton theorem and asymptotic symmetries in gravity in even dimensions $d=2+2m$ higher than four. After rewriting the subleading soft graviton theorem as a Ward identity, we argue that the charges of such identity generate Diff$(S^{2m})$. In order to show that, we propose suitable commutation relation among certain components of the metric fields. As a result, all Diff$(S^{2m})$ transformations are symmetries of gravitational scattering.

Isolated surfaces and symmetries of gravity

Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and paying attention to the maximal such symmetry could have important consequences to further elucidate the quantization of gravity. After establishing an algebraic off-shell derivation of the maximal closed subalgebra of the full bulk diffeomorphisms in the presence of an isolated corner, we show how to geometrically describe the latter and its embedding in spacetime, without constraining the geometry away from the corner, such as by assuming a foliation. The analysis encompasses arbitrary embedded surfaces, of generic codimensions $k$. The resulting corner algebra ${\cal A}_k$, calling $S$ the embedded surface and $M$ the bulk, is that of the group $(Diff(S)\ltimes GL(k,\mathbb{R}))\ltimes \mathbb{R}^k$. This result is independent of any dynamics or pseudo-Riemannian structure in the bulk. We then evaluate the Noether charges of ${\cal A}_2$ for Einstein-Hilbert dynamics and show that the Noether charge algebra gives a representation of the algebra ${\cal A}_2$, for finite proper distance corners in the bulk, while all other charges associated with $Diff(M)$ vanish.

Model-independent test of the parity symmetry of gravity with gravitational waves

Gravitational wave (GW) data can be used to test the parity symmetry of gravity by investigating the difference between left-hand and right-hand circular polarization modes. In this article, we develop a method to decompose the circular polarizations of GWs produced during the inspiralling stage of compact binaries, with the help of stationary phase approximation. The foremost advantage is that this method is simple, clean, independent of GW waveform, and is applicable to the existing detector network. Applying it to the mock data, we test the parity symmetry of gravity by constraining the velocity birefringence of GWs. If a nearly edge-on binary neutron-stars with observed electromagnetic counterparts at 40 Mpc is detected by the second-generation detector network, one could derive the model-independent test on the parity symmetry in gravity: the lower limit of the energy scale of parity violation can be constrained within mathcal {O}(10^4mathrm{eV}).

Analogous BMS symmetry in QED and quantum anomaly in Dirac and Weyl semimetals

We show that the asymptotic infinite dimensional enlarged gauge symmetries constructed for QED are anomalous in Weyl semimetals. This symmetry is particularly important in particle physics for its analogy with the Bondi–Metzner–Sachs (BMS) symmetries in gravity, as well as for its connection with QED soft IR theorems. This leads to observable effects, because of the induction of a new current in the material, which carries a memory of the BMS symmetry precursor.

Generalized BMS charge algebra

It has been argued that the symmetries of gravity at null infinity should include a Diff$(S^2)$ factor associated to diffeomorphisms on the celestial sphere. However, the standard phase space of gravity does not support the action of such transformations. Building on earlier work by Laddha and one of the authors, we present an extension of the phase space of gravity at null infinity on which Diff$(S^2)$ acts canonically. The Poisson brackets of supertranslation and Diff$(S^2)$ charges reproduce the generalized BMS algebra introduced in arXiv:1408.2228 .

Ehlers symmetry in four dimensions

Starting with the light-cone Hamiltonian for gravity, we perform a field redefinition that reveals a hidden symmetry in four dimensions, namely the Ehlers $SL(2,R)$ symmetry. The field redefinition, which is non-local in space but local in time, acts as a canonical transformation in the Hamiltonian formulation keeping the Poisson bracket relations unaltered. We discuss the electro-magnetic duality symmetry of gravity in the light-cone formalism, which forms the $SO(2)$ subgroup of the Ehlers symmetry. The helicity states in the original Hamiltonian are not in a representation of the enhanced symmetry group. In order to make the symmetry manifest, we make a change of variables in the path integral from the helicity states to new fields that transform linearly under the $SO(2)$ duality symmetry.

Waveform of gravitational waves in the general parity-violating gravities

As an extension of our previous work [J.Qiao, T.Zhu, W.Zhao & A.Wang, arXiv:1909.03815], in this article, we calculate the effects of parity violation on gravitational-wave (GW) waveforms during their propagation in the most general parity-violating gravities, including Chern-Simons modified gravity, ghost-free scalar-tensor gravity, symmetric teleparallel equivalence of GR theory, Ho\v{r}ava-Lifshitz gravity and so on. For this purpose, we consider the GWs generated by the coalescence of compact binaries and concentrate on the imprints of the parity violation in the propagation of GWs. With a unified description of GW in the theories of parity-violating gravity, we study the effects of velocity and amplitude birefringence on the GW waveforms. Decomposing the GWs into the circular polarization modes, the two birefringence effects exactly correspond to the modifications in phase and amplitude of GW waveforms respectively. We find that, for each circular polarization mode, the amplitude, phase and velocity of GW can be modified by both the parity-violating terms and parity-conserving terms in gravity. Therefore, in order to test the parity symmetry in gravity, we should compare the difference between two circular polarization modes, rather than measuring an individual mode. Combining two circular modes, we obtain the GW waveforms in the Fourier domain, and obtain the deviations from those in General Relativity. The GW waveforms derived in this paper are also applicable to the theories of parity-conserving gravity, which have the modified dispersion relations (e.g. massive gravity, double special relativity theory, extra-dimensional theories, etc), or/and have the modified friction terms (e.g. nonlocal gravity, gravitational theory with time-dependent Planck mass, etc).

Noncommutativity in near horizon symmetries in gravity

We have a new observation that near horizon symmetry generators, corresponding to diffeomorphisms which leave the horizon structure invariant, satisfy noncommutative Heisenberg algebra. The results are valid for any null surfaces (which have Rindler structure in the near null surface limit) and in any spacetime dimensions. Using the Sugawara construction technique the central charge is identified. It is shown that the horizon entropy is consistent with the standard form of the Cardy formula. Therefore we feel that the noncommutative algebra might lead to quantum mechanics of horizon and also can probe into the microscopic description of entropy.

The role of conformal symmetry in gravity and the standard model

In this paper we consider conformal symmetry in the context of manifolds with general affine connection. We extend the conformal transformation law of the metric to a general metric compatible affine connection, and find that it is a symmetry of both the geodesic equation and the Riemann tensor. We derive the generalised Jacobi equation and Raychaudhuri equation and show that they are both conformally invariant. Using the geodesic deviation (Jacobi) equation we analyse the behaviour of geodesics in different conformal frames. Since we find that our version of conformal symmetry is exact in classical pure Einstein's gravity, we ask whether one can extend it to the standard model. We find that it is possible to write conformal invariant Lagrangians in any dimensions for vector, fermion and scalar fields, but that such Lagrangians are only gauge invariant in four dimensions. Provided one introduces a dilaton field, gravity can be conformally coupled to matter.

Anisotropic cubic curvature couplings

To complement recent work on tests of spacetime symmetry in gravity, cubic curvature couplings are studied using an effective field theory description of spacetime-symmetry breaking. The associated mass dimension 8 coefficients for Lorentz violation studied do not result in any linearized gravity modifications and instead are revealed in the first nonlinear terms in an expansion of spacetime around a flat background. We consider effects on gravitational radiation through the energy loss of a binary system and we study two-body orbital perturbations using the post-Newtonian metric. Some effects depend on the internal structure of the source and test bodies, thereby breaking the Weak Equivalence Principle for self-gravitating bodies. These coefficients can be measured in solar-system tests, while binary-pulsar systems and short-range gravity tests are particularly sensitive.

Counterterms in gravity in the light-front formulation and a D = 2 conformal-like symmetry in gravity

In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N=8 Supergravity should work.

Dual symmetry and the vacuum energy

In this work we present a new hidden symmetry in gravity for the scale factor in the FRW model, for $k=0$. This exact symmetry vanishes the cosmological constant. We interpret this hidden symmetry as a dual symmetry in the sense that appears in the string theory.

Nongauge local symmetry in gravity

It is shown that there exists a class of nongauge local symmetry in gravity. It is the combination of the known gauge symmetries andδ off shell transformation.δ off shell is the transformation which vanishes on shell.δ off shell invariance imposes some restriction on model Lagrangians besides gauge symmetry, though it does not reduce the physical degrees of freedom.