Gravitational Corrections Research Articles

Quantum Gravitational Contributions to Gauge Field Theories

We revisit quantum gravitational contributions to quantum gauge field theories in the gauge condition independent Vilkovisky—DeWitt formalism based on the background field method. With the advantage of Landau-DeWitt gauge, we explicitly obtain the gauge condition independent result for the quadratically divergent gravitational corrections to gauge couplings. By employing, in a general way, a scheme-independent regularization method that can preserve both gauge invariance and original divergent behavior of integrals, we show that the resulting gauge coupling is power-law running and asymptotically free. The regularization scheme dependence is clarified by comparing with results obtained by other methods. The loop regularization scheme is found to be applicable for a consistent calculation.

On the interpretation of gravitational corrections to gauge couplings

Several recent papers discuss gravitational corrections to gauge couplings that depend quadratically on the energy. In the framework of the background-field approach, these correspond in general to adding to the effective action terms quadratic in the field strength but with higher-order space–time derivatives. We observe that such terms can be removed by appropriate local field redefinitions, and do not contribute to physical scattering-matrix elements. We illustrate this observation in the context of open string theory, where the effective action includes, among other terms, the well-known Born–Infeld form of non-linear electrodynamics. We conclude that the quadratically energy-dependent gravitational corrections are not physical in the sense of contributing to the running of a physically-measurable gauge coupling, or of unifying couplings as in string theory.

Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems

Using the first law of binary black-hole mechanics, we compute the binding energy E and total angular momentum J of two nonspinning compact objects moving on circular orbits with frequency Ω, at leading order beyond the test-particle approximation. By minimizing E(Ω) we recover the exact frequency shift of the Schwarzschild innermost stable circular orbit induced by the conservative piece of the gravitational self-force. Comparing our results for the coordinate-invariant relation E(J) to those recently obtained from numerical simulations of comparable-mass nonspinning black-hole binaries, we find a remarkably good agreement, even in the strong-field regime. Our findings confirm that the domain of validity of perturbative calculations may extend well beyond the extreme mass-ratio limit.

Spacetime rotation-induced Landau quantization

We investigate non-inertial and gravitational effects on quantum states in electromagnetic fields and present the analytic solution for energy eigenstates for the Schr\"odinger equation including non-inertial, gravitational and electromagnetic effects. We find that in addition to the Landau quantization the rotation of spacetime itself leads to the additional quantization, and that the energy levels for an electron are different from those for a proton at the level of gravitational corrections.

BLACK HOLES AND ASYMPTOTICALLY SAFE GRAVITY

Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short-distance physics is characterized by a nontrivial fixed point of the gravitational coupling. We find that a weakening of gravity implies a decrease of the event horizon, and the existence of a Planck-size black hole remnant with vanishing temperature and vanishing heat capacity. The absence of curvature singularities is generic and discussed together with the conformal structure and the Penrose diagram of asymptotically safe black holes. The production cross-section of mini-black holes in energetic particle collisions, such as those at the Large Hadron Collider, is analysed within low-scale quantum gravity models. Quantum gravity corrections imply that cross-sections display a threshold, are suppressed in the Planckian, and reproduce the semiclassical result in the deep trans-Planckian region. Further implications are discussed.

Gravitational instantons and fluxes from M/F-theory on Calabi-Yau fourfolds

We compactify four-dimensional N=1 gauged supergravity theories on a circle including fluxes for shift-symmetric scalars. Four-dimensional Taub-NUT gravitational instantons universally correct the three-dimensional superpotential in the absence of fluxes. In the presence of fluxes these Taub-NUT instanton contributions are no longer gauge-invariant. Invariance can be restored by gauge instantons on top of Taub-NUT instantons. We establish the embedding of this scenario into M-theory. Circle fluxes and gaugings arise from a restricted class of M-theory four-form fluxes on a resolved Calabi-Yau fourfold. The M5-brane on the base of the elliptic fourfold dualizes into the universal Taub-NUT instanton. In the presence of fluxes this M5-brane is anomalous. We argue that anomaly free contributions arise from involved M5-brane geometries dual to gauge-instantons on top of Taub-NUT instantons. Adding a four-dimensional superpotential to the gravitational instanton corrections leads to three-dimensional Anti-de Sitter vacua at stabilized compactification radius. We comment on the possibility to uplift these M-theory vacua, and to tunnel to four-dimensional F-theory vacua.

Quantum Gravitational Contributions to the Cosmic Microwave Background Anisotropy Spectrum

We derive the primordial power spectrum of density fluctuations in the framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field. In this way, we first recover the scale-invariant power spectrum that is found as an approximation in the simplest inflationary models. We then obtain quantum gravitational corrections to this spectrum and discuss whether they lead to measurable signatures in the cosmic microwave background anisotropy spectrum. The nonobservation so far of such corrections translates into an upper bound on the energy scale of inflation.

A nonlinear scalar model of extreme mass ratio inspirals in effective field theory: II. Scalar perturbations and a master source

The motion of a small compact object (SCO) in a background spacetime is investigated further in the context of a class of model nonlinear scalar field theories that have a perturbative structure analogous to the general relativistic description of extreme mass ratio inspirals. We derive regular expressions for the scalar perturbations generated by the motion of the compact object that are valid through third order in ε the size of the SCO to the background curvature length scale. Our results for the field perturbations are compared to those calculated through second order in ε by Rosenthal (2005 Class. Quantum Grav. 22 S859) and found to agree. However, our procedure for regularizing the scalar perturbations is considerably simpler. Following the Detweiler–Whiting scheme, we use our results for the regular expressions for the field and derive the regular self-force corrections through third order. We find agreement with our previous derivation based on a variational principle of an effective action for the worldline associated with the SCO thereby demonstrating the internal consistency of our formalism. This also explicitly demonstrates that the Detweiler–Whiting decomposition of Green’s functions is a valid and practical method of self-force computation at higher orders in perturbation theory and more generally, at all orders in perturbation theory, as we show in an appendix. Finally, we identify a central quantity, which we call a master source, from which all other physically relevant quantities are derivable. Specifically, knowing the master source through some order in ε allows one to construct the waveform measured by an observer, the regular part of the field and its derivative on the worldline, the regular part of the self-force and various orbital quantities such as shifts of the innermost stable circular orbit, etc when restricting to conservative dynamics. The existence of a master source together with the regularization methods implemented in this series should be indispensable for derivations of higher order gravitational self-force corrections in the future.

Thermodynamics of Vaidya-Bonner-de Sitter space time based on the generalized space-time uncertainty

In each static or stationary space time k is just surface gravity of the horizon, but in the of Vaidya-Bonner-de Sitter space time, it is no longer the surface gravity of the event horizon. This property makes the Vaidya-Bonner as an important horizon. In this paper, the entropy of Vaidya-Bonner-de Sitter space time is calculated. In continue, employing the generalized uncertainty principle, quantum gravitational corrections to the entropy of Vaidya-Bonner space time is studied.

Gravitational corrections to fermion masses in grand unified theories

We reconsider quantum gravitational threshold corrections to the unification of fermion masses in grand unified theories. We show that the running of the Planck mass can have a sizable effect on these thresholds that are thus much more important than naively expected. These corrections make any extrapolation from low energy measurements challenging.

Gravitational Corrections to Non-Gauge Interactions

We compute the lowest order quantum gravitational corrections to Yukawa and ϕ 4 interactions.

Gauge-invariant quantum gravity corrections to Callan-Symanzik beta functions via the Vilkovisky-DeWitt method and gravity-assisted gauge unification

Gravity is the weakest force in nature, and the gravitational interactions with all standard model (SM) particles can be well described by perturbative expansions of the Einstein-Hilbert action as an effective theory, all the way up to energies below the fundamental Planck scale. We use Vilkovisky-DeWitt method to derive the first gauge-invariant nonzero gravitational power-law corrections to the running of gauge couplings, which make both Abel and non-Abel gauge interactions asymptotically free. We further demonstrate that the graviton-induced universal power-law runnings always assist the three SM gauge forces to reach unification around the Planck scale, irrespective of the detail of logarithmic corrections. We also compute the power-law corrections to the SM Higgs sector and derive modified triviality bound on the Higgs boson mass.

Running couplings and operator mixing in the gravitational corrections to coupling constants

The use of a running coupling constant in renormalizable theories is well known, but the implementation of this idea for effective field theories with a dimensional coupling constant is, in general, less useful. Nevertheless, there are multiple attempts to define running couplings, including the effects of gravity, with varying conclusions. We sort through many of the issues involved, most particularly the idea of operator mixing and also the kinematics of crossing, using calculations in Yukawa and $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ theories as illustrative examples. We remain in the perturbative regime. In some theories with a high permutation symmetry, such as $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$, a reasonable running coupling can be defined. However, in most cases, such as Yukawa and gauge theories, a running coupling fails to correctly account for the energy dependence of the interaction strength. As a by-product we also contrast on-shell and off-shell renormalization schemes and show that operators which are normally discarded, such as those that vanish by the equations of motion, are required for off-shell renormalization of effective field theories. Our results suggest that the inclusion of gravity in the running of couplings is not useful or universal in the description of physical processes.

Wilsonian approach to fluid/gravity duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty)$ reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant $D(horizon)$ reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $\eta /s$ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.

Neutrino oscillations in the gravitational field

We calculate the gravitational correction to the phase difference between neutrino mass eigenstates for the spherically symmetric gravitational field described by the Schwarzschild metric. This correction was calculated in a number of works, but the results of these works differ from each other. Our result does not coincide with the results ever published. In this work, we make calculations in the simplest way and verify our result by several tests.

Gravitational Contributions to Running of Gauge Couplings

Gravitational contributions to the running of gauge couplings are calculated by using different regularization schemes. As the β function concerns counter-terms of dimension four, only quadratic divergences from the gravitational contributions need to be investigated. A consistent result is obtained by using a symmetry-preserving loop regularization with string-mode regulators which can appropriately treat the quadratic divergences and preserve non-abelian gauge symmetry. The harmonic gauge condition for gravity is used in both diagrammatical and background field calculations, the resulting gravitational corrections to the β function are found to be nonzero, which is different from previous results presented in the existing literatures.

Quantum gravitational correction to the Hawking temperature from the Lemaître-Tolman-Bondi model

We solve the quantum constraint equations of the Lema\^{\i}tre-Tolman-Bondi model in a semiclassical approximation in which an expansion is performed with respect to the Planck length. We recover in this way the standard expression for the Hawking temperature as well as its first quantum gravitational correction. We then interpret this correction in terms of the one-loop trace anomaly of the energy-momentum tensor and thereby make contact with earlier work on quantum black holes.

Holomorphicity and modularity in Seiberg-Witten theories with matter

We calculate the gravitational corrections to the effective action of N=2 SU(2) Seiberg-Witten theory with matter using modularity, the holomorphic anomaly equation and expected behavior at the boundaries of the moduli space. As in pure gauge theory we show that the gap condition at the dyon singularities completely fixes the gravitational corrections. We discuss the behavior of the gravitational corrections at the conformal points. We compare our results with the recursive solution of the loop equation in the matrix model approach, which provides in addition open amplitudes.

Hybrid natural low scale inflation

We discuss the phenomenological implications of Hybrid Natural Inflation models in which the inflaton is a pseudo-Goldstone boson but inflation is terminated by a second scalar field. A feature of the scheme is that the scale of breaking of the Goldstone symmetry can be lower than the Planck scale and so gravitational corrections are under control. We show that, for supersymmetric models, the scale of inflation can be chosen anywhere between the Lyth upper bound and a value close to the electroweak breaking scale. The observed density perturbations and spectral index are readily obtained by the choice of the free parameters. The tensor to scalar ratio and the spectral tilt are extremely small.

Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length

The (D+1)-dimensional (β,β′)-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk (J. Phys., A Math. Gen. 39, 10909, 2006), leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′=2β up to first order over deformation parameter β. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes two massive particles with different masses. We have shown that physically acceptable mass states can only exist for $\beta<\frac{1}{8m^{2}c^{2}}$ which leads to an isotropic minimal length in the interval 10−17 m<(ΔX i )0<10−15 m. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.