Frame-like action and unfolded formulation for massive higher-spin fields

Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS$(A)\mathit{dS}$ spaces are presented. Manifestly gauge invariant action for a spin s?2$s?2$ massive field in any dimension is constructed in terms of gauge invariant curvatures.     

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.     

On the models of gravitational fields

Modelling of the gravitational field is discussed within the framework of Einstein's theory. Modelling is defined as the mapping whereby the geodesic lines (the path of test bodies) go into the family of curves given by the equation of a test body motion in a model. Different possible ways of modelling are singled out — namely, the complete, selective, and approximate-selective ones. The theory is applied to the solar gravitational field.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971. Professor Petrov died in the Summer of 1972. He was one of the members of the International Committee on GRG and founder of the Journal on GRG. We are happy to publish this contribution of his and shall respectfully keep him in our memory. (The Editor.)     

Cubic interaction vertex of higher-spin fields with external electromagnetic field

We fulfill the detailed analysis of coupling the charged bosonic higher-spin fields to external constant electromagnetic field in first order in external field strength. Cubic interaction vertex of arbitrary massive and massless bosonic higher-spin fields with external field is found. Construction is based on deformation of free Lagrangian and free gauge transformations by terms linear in electromagnetic field strength. In massive case a formulation with Stueckelberg fields is used. We begin with the most general form of deformations for Lagrangian and gauge transformations, admissible by Lorentz covariance and gauge invariance and containing some number of arbitrary coefficients, and require the gauge invariance of the deformed theory in first order in strength. It yields the equations for the coefficients which are exactly solved. As a result, the complete interacting Lagrangian of arbitrary bosonic higher-spin fields with constant electromagnetic field in first order in electromagnetic strength is obtained. Causality of massive spin-2 and spin-3 fields propagation in the corresponding electromagnetic background is proved.     

A note on self-dual gravitational fields

In this note we give two new simple derivations of the good-cut equation, the equation which governs (complex) self-dual asymptotically flat gravitational fields. One of these derivations is remarkably simple, involving only a few lines. Our main point of interest, however, is in the second derivation. Though it is slightly more complicated, this method of derivation is almost certainly generalizable to cover real asymptotically flat space-times and thus lead to a generalization of the good-cut equation.     

The content of unitarity constraints on a pomeron pole of intercept one

We present a consistent picture of a pomeron pole with intercept one, together with its cuts, which evades the decoupling arguments. We use the reggeon cut discontinuity formulae to introduce Gribov's reggeon calculus as an exact solution of multiparticle t-channel unitarity. We show how, within the calculus, two-pomeron iterations of a singular kernel can be responsible for the zero in the triple-pomeron vertex. Using the concept of a bare pomeron pole as a multiperipheral production process which is subsequently renormalised by other effects, we apply the reggeon calculus analysis to inclusive cross sections. We find that the inclusive sum rule decoupling arguments are avoided because of the addition of enhanced absorptive corrections to the conventional Regge pole contributions. However, we show that in this picture the combined pole and two-pomeron cut contribution to the total cross section factories to order (ln s)^?2.We also show that, when the correct helicity structure of the pomeron is taken into account, the s-channel unitarity condition for pomeron scattering amplitudes does not lead to any serious decouplings.     

On partition function and Weyl anomaly of conformal higher-spin fields

We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s   fields, generalizing the previously known expression for the 1-loop Weyl graviton (s=2$s=2$) partition function. We compute the corresponding spin s   Weyl anomaly coefficients _as${\mathrm{a}}_s$ and _cs${\mathrm{c}}_s$. Our result for _as${\mathrm{a}}_s$ reproduces the expression found recently in arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S⁴$S^4$ to a ratio of known partition functions of massless higher-spin field in AdS₅ with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the bosonic _as${\mathrm{a}}_s$ coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case.     

Effect of massive fields on inflation

Effects caused by an additional massive scalar field interacting with an inflaton field are analyzed. Inflation is shown to have two stages, the first of which is dominant and characterized by ultraslow dynamics of the inflaton field. Constraints on the model parameters are obtained.     

On the theory of inertial gravitational fields

The generalized equations of the inertial gravitational field are derived from variational principles. It is shown that variational properties of inertial gravitational potentials have important peculiarities which cause peculiarities of equations obtained.     

Strong gravitational lensing constraints on holographic dark energy

Strong gravitational lensing(SGL) has provided an important tool for probing galaxies and cosmology. In this paper, we use the SGL data to constrain the holographic dark energy model, as well as models that have the same parameter number, such as the w CDM and Ricci dark energy models. We find that only using SGL is difficult to effectively constrain the model parameters.However, when the SGL data are combined with CBS(CMB+BAO+SN) data, the reasonable estimations can be given and the constraint precision is improved to a certain extent, relative to the case of CBS only. Therefore, SGL is an useful way to tighten constraints on model parameters.