Gauge fields and inflation

The isotropy and homogeneity of the cosmic microwave background (CMB) favors “scalar driven” early Universe inflationary models. However, gauge fields and other non-scalar fields are far more common at all energy scales, in particular at high energies seemingly relevant to inflation models. Hence, in this review we consider the role and consequences, theoretical and observational, that gauge fields can have during the inflationary era. Gauge fields may be turned on in the background during inflation, or may become relevant at the level of cosmic perturbations. There have been two main classes of models with gauge fields in the background, models which show violation of the cosmic no-hair theorem and those which lead to isotropic FLRW cosmology, respecting the cosmic no-hair theorem. Models in which gauge fields are only turned on at the cosmic perturbation level, may source primordial magnetic fields. We also review specific observational features of these models on the CMB and/or the primordial cosmic magnetic fields. Our discussions will be mainly focused on the inflation period, with only a brief discussion on the post inflationary (p)reheating era.     

Hidden Variables and the Nature of Quantum Statistics

It is shown that the nature of quantum statistics can be clarified by assuming the existence of a background of random gravitational fields and waves, distributed isotropically in space. This background is responsible for correlating phases of oscillations of identical microobjects. If such a background of random gravitational fields and waves is considered as hidden variables, then taking it into account leads to Bell-type inequalities that are fairly consistent with experimental data.     

General background field calculations with fermion fields

Background field calculations including fermion background fields are undertaken to determine one- and two-loop counterterms, and β-functions, for a general vector, scalar, spinor field gauge theory. Dimensional regularisation, and also the dimensional reduction variant, with a non-perturbative treatment of the background fields are used. In the dimensional reduction case two alternative forms are given for the results depending on the precise treatment of ε-scalars.     

Staggered fermions and rotation-gauge invariance

We study the rotational invariance of the staggered fermions on the lattice by considering them as spin-zero fields in a quenched gauge field background. The non-integer spin fermionic fields are reconstructed. Bilinear operators (i.e. meson fields) in terms of the quark fields on a cube are classified according to the representations of the discrete rotational group.     

Emergent polarization singularities

Polarization singularities are shown to emerge spontaneously from the incoherent addition of uncorrelated optical fields that individually need not contain singularities. Examples of this phenomenon are given for both vector and ellipse fields. The incoherent addition of vector fields whose singularities have integer winding numbers is shown to yield fields whose singularities have half-integer winding numbers. These findings are used to make predictions about the singularities of the polarized component of the cosmic microwave background.     

BRST current and anomalies in spinning string in background fields

Calculation of the super Jacobian of the holomorphic Becchi-Rouet-Stora-Tyutin (BRST) transformations of the path-integral functional measure of the spinning string variable and its ghosts in presence of background fields is undertaken in order to obtain BRST current identity and related anomalies. The free BRST current identity is obtained only if the background fields satisfy the equations of motion. In this case the superconformal factor decouples from the background fields and it is possible to incorporate the super Liouville action.     

Non-renormalization of induced charges and constraints on strongly coupled theories

It is shown that global fermionic charges induced in vacuum by slowly varying, topologically non-trivial background scalar fields are not renormalized provided that expansion in momenta of background fields is valid. This suggests that strongly coupled theories obey induced charge matching conditions which are analogous, but generally not equivalent, to 't Hooft anomaly matching conditions. We give a few examples of induced charge matching. In particular, the corresponding constraints in softly broken supersymmetric QCD suggest non-trivial low-energy mass pattern, in full accord with the results of direct analyses.     

Hadronic Correction to Coulomb Potential Between Quarks and Diquark Structure

We have studied the hadronic correction from the background pion fields due to the chiral symmetry breaking to the Coulomb potential that governs the short-distance behavior of the interactions between the bound quarks. The background fields are associated with the constituent quark mass. We find a modified potential form which favors the diquark structure. We also roughly estimate an influence of this correction on the phase shifts in nucleon-nucleon scattering and find that it may cause an extra middle range attraction between nucleons which is expected.     

Multiple fundamental strings and waves to non-linear order in the background fields

The Chern–Simons actions of the multiple fundamental string and the multiple gravitational wave are established to full order in the background fields. Gauge invariance is checked. Special attention is drawn to the non-Abelian gauge transformations of the world-volume fields.     

Magnetovacs in gauged N = 4 supergravity

A two-parameter family of supersymmetric background field solutions of the recently formulated version of gauged N = 4 supergravity is found. This constitutes strong evidence that the theory has stable vacua, despite energy densities that are unbounded below. The background geometries are metric products of (AdS)₂ × S₂, and there are covariantly constant magnetic and electric fields. For a special choice of parameters the (AdS)₂ factor becomes a flat Minkowski space and electric fields vanish.     

Classification of Surface Charges for a Spin 2 Field on a Curved Background Solution

Within the framework of local BRST cohomology, we establish that nontrivial conserved n– 2 forms for a spin 2 field on a background corresponding to a solution to Einstein's equation with or without cosmological constant are characterized uniquely by the Killing vector fields of the background. This result is crucial in various applications in gravitation, in particular for the study of consistent interactions of spin 2 fields on curved backgrounds. It provides a nontrivial generalization of an analogous result proved in the flat case.     

Beta functions and S-matrix in string theory

The relationship between sigma model β-functions and string theory scattering amplitudes is proved. We derive our results for the closed bosonic string using the weak field expansion around the flat space. The equations of motion for all the background fields, including the heavy fields are considered. We show that the effective equations for the light fields are obtained by integrating out the heavy fields. It is shown that the contributions to the β-functions come from the boundary of moduli space on a punctured Riemann surface. String loop corrections to the equations of motion are also studied.     

Non-abelian gauge theories in a background field

Green functions of on-mass-shell transverse gauge fields in a background gauge are proved to be obtained from Green functions in the perturbative vacuum by a mere translation.     

Cosmological magnetic fields

Magnetic fields are observed not only in stars, but in galaxies, clusters, and even high redshift Lyman-α systems. In principle, these fields could play an important role in structure formation and also affect the anisotropies in the cosmic microwave background radiation (CMB). The study of cosmological magnetic fields aims not only to quantify these effects on large-scale structure and the CMB, but also to answer one of the outstanding puzzles of modern cosmology: when and how do magnetic fields originate? They are either primoridial, i.e. created before the onset of structure formation, or they are generated during the process of structure formation itself.     

Flag-dipole and flagpole spinor fluid flows in Kerr spacetimes

Flagpole and flag-dipole spinors are particular classes of spinor fields that has been recently used in different branches of theoretical physics. In this paper, we study the possibility and consequences of these spinor fields to induce an underlying fluid flow structure in the background of Kerr spacetimes. We show that flag-dipole spinor fields are solutions of the equations of motion in this context. To our knowledge, this is the second time that this class of spinor field appears as a physical solution, the first one occurring as a solution of the Dirac equation in ESK gravities.     

Magnetic monopole solutions of non-Abel gauge theory in an expanding universe

The equations of motion of Yang-Mills-Higgs fields are considered within the framework of the SO(3) model against the background of the gravitational fields of an expanding universe. Static and nonstatic Bogomolov-Prasad-Sommerfield magnetic monopole solutions are found for various laws of gravitational field evolution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 67–71, August, 1984.     

Open bosonic strings in general background fields

We discuss the renormalization properties of the 2 dim. field theory describing an open bosonic string in the background fields corresponding to its massless excitations. The relevant β-functions are calculated for gravitational, antisymmetric tensor and Yang-Mills background on 1-loop level, for pure Yang-Mills background an 2-loop level and in the Abelian case up to 3 loops. We find a renormalization scheme dependence starting at 2 loop order. Putting β to zero yields the equation of motion for the non-linear electrodynamics of Fradkin and Tseytlin.     

Spin–gravity coupling and gravity-induced quantum phases

External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the study of spin–gravity coupling and of the optics of particles in gravitational or inertial fields. We discuss the role that spin–gravity coupling plays in particular problems.