Vector Gauge Fields Research Articles

Stability of a tachyon braneworld

Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional warped gravity with some matter content, braneworld models must prove to be stable under the whole set of small fluctuations of the gravitational and matter fields background, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tachyonic thick braneworlds with an embedded maximally symmetric 4D space-time, revealing its physical consistency. This family of models contains a recently reported tachyonic de Sitter thick braneworld which possesses a series of appealing properties. These features encompass complete regularity, asymptotic flatness (instead of being asymptotically dS or AdS) even when it contains a negative bulk cosmological constant, a relevant 3-brane with dS metric which naturally arises from the full set of field equations of the 5D background (it is not imposed), qualitatively describing the inflationary epochs of our Universe, and a graviton spectrum with a single zero mode bound state that accounts for the 4D graviton localised on the brane and is separated from the continuum of Kaluza-Klein massive graviton excitations by a mass gap. The presence of this mass gap in the graviton spectrum makes the extra-dimensional corrections to Newton's law decay exponentially. Gauge vector fields with a single massless bound state in its mass spectrum are also localised on this braneworld model a fact that allows us to recover the Coulomb's law of our 4D world. All these properties of the above referred tachyonic braneworld together with the positive stability analysis provided in this work, constitute a firm step towards the construction of realistic cosmological models within the braneworld paradigm.

Gauge fields in a string-cigar braneworld

In this work, we investigate the properties of the Abelian gauge vector field in the background of a string-cigar braneworld. Both the thin and thick brane limits are considered. The string-cigar scenario can be regarded as an interior and exterior string-like solution. The source undergoes a geometric Ricci flow which is related to a variation of the bulk cosmological constant. The Ricci flow changes the width and amplitude of the massless mode at the brane core and recovers the usual string-like behavior at large distances. By means of suitable numerical methods, we attain the Kaluza–Klein (KK) spectrum for the string-like and the string-cigar models. For the string-cigar model, the KK modes are smooth near the brane and their amplitude are enhanced by the brane core. Furthermore, the analogue Schrödinger potential is also regulated by the geometric flow.

Can spin-charge-family theory explain baryon number nonconservation?

The spin-charge-family theory, in which spinors carry besides the Dirac spin also the second kind of the Clifford object, no charges, is a kind of the Kaluza-Klein theories. The Dirac spinors of one Weyl representation in $d=(13+1)$ manifest in $d=(3+1)$ at low energies all the properties of quarks and leptons assumed by the standard model. The second kind of spins explains the origin of families. Spinors interact with the vielbeins and the two kinds of the spin connection fields, the gauge fields of the two kinds of the Clifford objects, which manifest in $d=(3+1)$ besides the gravity and the known gauge vector fields also several scalar gauge fields. Scalars with the space index $s\in (7,8)$ carry the weak charge and the hyper charge ($\mp \frac{1}{2}, \pm \frac{1}{2}$, respectively), explaining the origin of the Higgs and the Yukawa couplings. It is demonstrated in this paper that the scalar fields with the space index $t\in (9,10,\dots,14)$ carry the triplet colour charges, causing transitions of antileptons and antiquarks into quarks and back, enabling the appearance and the decay of baryons. These scalar fields are offering in the presence of the right handed neutrino condensate, which breaks the ${\cal C}{\cal P}$ symmetry, the answer to the question about the matter-antimatter asymmetry.

New localization method of U(1) gauge vector field on flat branes in (asymptotic) AdS5 spacetime

It is well known that the gauge vector field, with standard five-dimensional (5D) action, cannot be localized on Randall–Sundrum-like braneworlds with an infinite extra dimension. In this paper, we propose a modified 5D action to localize the gauge vector field on flat branes with an infinite or finite extra dimension. The localization method is realized by adding a dynamical mass term into the standard 5D action of the vector field, which is proportional to the 5D scalar curvature. It is shown that the vector zero mode is localizable if the 5D spacetime is (asymptotic) AdS5. Moreover, the massive tachyonic modes can be excluded.

The Explanation for the Origin of the Higgs Scalar and for the Yukawa Couplings by the <i>Spin-Charge-Family</i> Theory

The spin-charge-family theory is a kind of the Kaluza-Klein theories, but with two kinds of the spin connection fields, which are the gauge fields of the two kinds of spins. The SO(13,1) representation of one kind of spins manifests in d = (3 + 1) all the properties of family members as assumed by the standard model; the second kind of spins explains the appearance of families. The gauge fields of the first kind, carrying the space index m = (0,...,3), manifest in d = (3 + 1) all the vector gauge fields assumed by the standard model. The gauge fields of both kinds of spins, which carry the space index (7, 8) gaining at the electroweak break nonzero vacuum expectation values, manifest in d = (3 + 1) as scalar fields with the properties of the Higgs scalar of the standard model with respect to the weak and the hyper charge ( and , respectively), while they carry additional quantum numbers in adjoint representations, offering correspondingly the explanation for the scalar Higgs and the Yukawa couplings, predicting the fourth family and the existence of several scalar fields. The paper 1) explains why in this theory the gauge fields are with the scalar index s = (5,6,7,8) doublets with respect to the weak and the hyper charge, while they are with respect to all the other charges in the adjoint representations; 2) demonstrates that the spin connection fields manifest as the Kaluza-Klein vector gauge fields, which arise from the vielbeins; and 3) explains the role of the vielbeins and of both kinds of the spin connection fields.

On brane symmetries

The geometric approach to branes is reformulated in terms of gauge vector fields interacting with massless tensor multiplets in gravitational backgrounds

Constraints on gauge field production during inflation

In order to gain new insights into the gauge field couplings in the early universe, we consider the constraints on gauge field production during inflation imposed by requiring that their effect on the CMB anisotropies are subdominant. In particular,we calculate systematically the bispectrum of the primordial curvature perturbation induced by the presence of vector gauge fields during inflation. Using a model independent parametrization in terms of magnetic non-linearity parameters, we calculate for the first time the contribution to the bispectrum from the cross correlation between the inflaton and the magnetic field defined by the gauge field. We then demonstrate that in a very general class of models, the bispectrum induced by the cross correlation between the inflaton and the magnetic field can be dominating compared with the non-Gaussianity induced by magnetic fields when the cross correlation between the magnetic field and the inflaton is ignored.

Scalar gauge fields

In this paper we give a variation of the gauge procedure which employs a scalar gauge field, $B (x)$, in addition to the usual vector gauge field, $A_\mu (x)$. We study this variant of the usual gauge procedure in the context of a complex scalar, matter field $\phi (x)$ with a U(1) symmetry. We will focus most on the case when $\phi$ develops a vacuum expectation value via spontaneous symmetry breaking. We find that under these conditions the scalar gauge field mixes with the Goldstone boson that arises from the breaking of a global symmetry. Some other interesting features of this scalar gauge model are: (i) The new gauge procedure gives rise to terms which violate C and CP symmetries. This may have have applications in cosmology or for CP violation in particle physics; (ii) the existence of mass terms in the Lagrangian which respect the new extended gauge symmetry. Thus one can have gauge field mass terms even in the absence of the usual Higgs mechanism; (iii) the emergence of a sine-Gordon potential for the scalar gauge field; (iv) a natural, axion-like suppression of the interaction strength of the scalar gauge boson.

Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

We show that fermion charge fractionalization can take place in a recently proposed chiral gauge model for graphene even in the absence of Kekul\'e distortion in the graphene honeycomb lattice. In this model, electrons couple in a chiral way to a pseudomagnetic field with a vortex profile in such a way that it can be used to describe the influences of topological defects, such as disclinations, on the electronic states. We also extend the model by adding the coupling of fermions to an external magnetic field and show that the fermion charge can be fractionalized by means of only gauge potentials. It is shown that the chiral fermion charge can also have fractional value. We also relate the fractionalization of the fermion charge to the parity anomaly in an extended quantum electrodynamics, which involves vector and axial-vector gauge fields.

Localization of gauge fields in a tachyonic de Sitter thick braneworld

In this work we show that universal gauge vector fields can be localized on the recently proposed 5D thick tachyonic braneworld which involves a de Sitter cosmological background induced on the 3-brane. Namely, by performing a suitable decomposition of the vector field, the resulting 4D effective action corresponds to a massive gauge field, while the profile along the extra dimension obeys a Schroedinger-like equation with a Poeschl-Teller potential. It turns out that the massless zero mode of the gauge field is bound to the expanding 3-brane and allows us to recover the standard 4D electromagnetic phenomena of our world. Moreover, this zero mode is separated from the continuum of Kaluza-Klein (KK) modes by a mass gap determined by the scale of the expansion parameter. We also were able to analytically solve the corresponding Schroedinger-like equation for arbitrary mass, showing that KK massive modes asymptotically behave like plane waves as expected.

TOPOLOGICAL EFFECTIVE FIELD THEORIES FOR DIRAC FERMIONS FROM INDEX THEOREM

Dirac fermions have a central role in high energy physics but it is well-known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the topological effective actions of (3+1)-massless Dirac fermions living on general backgrounds and coupled with vector and axial-vector gauge fields. The first step of our strategy is standard (in the Hermitian case) and consists in connecting the determinants of Dirac operators with the corresponding analytical indices through the zeta-function regularization. Then, we introduce a suitable splitting of the heat kernel that naturally selects the purely topological part of the determinant (i.e., the topological effective action). This topological effective action is expressed in terms of gauge fields using the Atiyah–Singer index theorem which computes the analytical index in topological terms. The main new result of this paper is to provide a consistent extension of this method to the non-Hermitian case, where a well-defined determinant does not exist. Quantum systems supporting relativistic fermions can thus be topologically classified on the basis of their response to the presence of (external or emergent) gauge fields through the corresponding topological effective field theories (TEFTs).

External sources in Lee-Wick theories

We investigate some peculiar aspects of the so called Lee-Wick Electrodynamics focusing on physical effects produced by the presence of sources for the vector field. The interactions between stationary charges distributions along parallel branes with arbitrary dimensions is investigated and the energy of a point charge is discussed. Some physical phenomena produced in the vicinity of a Dirac string are also investigated. We consider the Lee-Wick theory for the scalar field, where it can emerge some interesting effects with no counterpart for the vector gauge field theory.

Stability of Horndeski vector-tensor interactions

We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M2, that controls the strength of the non-minimal coupling.We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M2 > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term.We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.

Chiral conductivities and effective field theory

We construct the three-dimensional effective field theory which reproduces low-momentum static correlation functions in four-dimensional quantum field theories with U(1) axial anomalies and a dynamical vector gauge field, in thermal equilibrium. We compute radiative corrections to parity-violating chiral conductivities, to leading order in the effective theory. All of the anomaly-induced transport is susceptible to radiative corrections, except for certain two-point functions which are required by symmetry to vanish.

Pseudoscalar N-flation and axial coupling revisited

We revisit the dynamics of the axial coupling between many N-flatons and an Abelian gauge field, with special attention to its statistically anisotropic signal. The anisotropic power spectrum of curvature perturbations associated with the large-wavelength modes of the gauge vector field is generally undetectable, since the anisotropy is confined to small scales. If the gauge field is the electromagnetic field, provided that the number of fields participating in the exponential expansion is large, it could be possible to generate sizable large-scale magnetic fields. However, its spectrum is blue, and appreciable power on large scales implies an overly strong field on smaller scales, incompatible with observations. Furthermore, the anisotropy is also markedly enhanced, and might be at odds with the isotropic observed sky. These aspects further demand that the scale of inflation be kept to a minimum.

Spin and Orbital Angular Momentum of the Tensor Gauge Field

Following the recent studies of the trickiness in spin and orbital angular momentum of the vector gauge fields, we perform here a parallel analysis for the tensor gauge field, which has certain relation to gravitation. Similarly to the vector case, we find a nice feature that after removing all gauge degrees of freedom the angular momentum of the tensor gauge field vanishes for a stationary system. This angular momentum also shows a one-parameter invariance over the infinitely many ways of complete gauge fixing for the tensor field. The tensor gauge coupling, however, does exhibit a critical difference from the vector gauge coupling that it may induce intrinsic interaction terms into the spatial translation and rotation generators, leaving none of the ten Poincare generators interaction-free.

The anisotropy of a three- and a one-form

We calculate the anisotropic signal associated with the coupling of a three-form with an Abelian vector gauge field. In the simplest examples of three-form inflation the amplification of the vector fluctuations is exponential; this makes it almost certain that a large anisotropy will develop, severely constraining the viability of the coupling.

Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions

The monodromy transform and corresponding integral equation method described here give rise to a general systematic approach for solving integrable reductions of field equations for gravity coupled bosonic dynamics in string gravity and supergravity as well as for pure vacuum gravity in four and higher dimensions. For physically different types of fields in space-times of $D\ensuremath{\ge}4$ dimensions with $d=D\ensuremath{-}2$ commuting isometries---stationary fields with spatial symmetries, interacting waves or evolution of partially inhomogeneous cosmological models---the string gravity equations govern the dynamics of interacting gravitational, dilaton, antisymmetric tensor, and any number $n\ensuremath{\ge}0$ of Abelian vector gauge fields (all depending only on two coordinates). The equivalent spectral problem constructed earlier allows one to parametrize the entire infinite-dimensional space of (normalized) local solutions of these equations by two pairs of arbitrary coordinate-independent holomorphic $d\ifmmode\times\else\texttimes\fi{}d$- and $d\ifmmode\times\else\texttimes\fi{}n$- matrix functions ${{\mathbf{u}}_{\ifmmode\pm\else\textpm\fi{}}(w),{\mathbf{v}}_{\ifmmode\pm\else\textpm\fi{}}(w)}$ of a spectral parameter $w$ which constitute a complete set of monodromy data for a normalized fundamental solution of this spectral problem. The ``direct'' and ``inverse'' problems of such monodromy transform---calculating the monodromy data for any local solution and constructing the field configurations for any chosen monodromy data---always admit unique solutions. We construct the linear singular integral equations which solve this inverse problem. For any rational and analytically matched [i.e. ${\mathbf{u}}_{+}(w)\ensuremath{\equiv}{\mathbf{u}}_{\ensuremath{-}}(w)$ and ${\mathbf{v}}_{+}(w)\ensuremath{\equiv}{\mathbf{v}}_{\ensuremath{-}}(w)$] monodromy data the solution of these integral equations and corresponding solution for string gravity equations can be found explicitly. Simple reductions of the space of monodromy data leads to the similar constructions for solving of other integrable symmetry reduced gravity models, e.g. 5D minimal supergravity or vacuum gravity in $D\ensuremath{\ge}4$ dimensions.

Gauge vector field localization on a 3-brane placed in a warped transverse resolved conifold

We have investigated the features of the gauge vector field in a braneworld scenario built as a warped product between a 3-brane and a 2-cycle of the resolved conifold. This scenario allowed us to study how the gauge field behaves when the transverse manifold evolves upon a geometric flow that controls the singularity at the origin. Besides, since the transverse manifold has a cylindrical symmetry according to the 3-brane, this geometry can be regarded as a near brane correction of the string-like branes. Indeed, by means of a new warp function and the angular metric component of the resolved conifold, the braneworld can exhibit a conical form near the origin as well as a regular behavior in that region. The analysis of the gauge field in this background has been carried out for the s-wave state and a normalizable massless mode was found. For the massive modes, the resolution parameter avoids an infinite well on the brane and controls the depth of the well and the high of the barrier around the brane. The massive modes are slightly changed near the brane but they agreed with the string-like spectrum for large distances.

NONTRIVIAL GHOSTS AND SECOND-CLASS CONSTRAINTS

In a model in which a vector gauge field [Formula: see text] is coupled to an antisymmetric tensor field [Formula: see text] possessing a pseudoscalar mass, it has been shown that all physical degrees of freedom reside in the vector field. Upon quantizing this model using the Faddeev–Popov procedure, explicit calculation of the two-point functions 〈ϕϕ〉 and 〈Wϕ〉 at one-loop order seems to have yielded the puzzling result that the effective action generated by radiative effects has more physical degrees of freedom than the original classical action. In this paper we point out that this is not in fact a real effect, but rather appears to be a consequence of having ignored a "ghost" field arising from the contribution to the measure in the path integral arising from the presence of nontrivial second-class constraints. These ghost fields couple to the fields [Formula: see text] and [Formula: see text], which makes them distinct from other models involving ghosts arising from second-class constraints (such as massive Yang–Mills (YM) models) that have been considered, as in these other models such ghosts decouple. As an alternative to dealing with second-class constraints, we consider introducing a "Stueckelberg field" to eliminate second-class constraints in favor of first-class constraints and examine if it is possible to then use the Faddeev–Popov quantization procedure. In the Proca model, introduction of the Stueckelberg vector is equivalent to the Batalin–Fradkin–Tyutin (BFT) approach to converting second-class constraints to being first-class through the introduction of new variables. However, introduction of a Stueckelberg vector is not equivalent to the BFT approach for the vector–tensor model. In an appendix, the BFT procedure is applied to the pure tensor model and a novel gauge invariance is found. In addition, we also consider extending the Hamiltonian so that half of the second-class constraints become first-class and the other half become associated gauge conditions. We also find for this tensor-vector theory that when converting the phase space path integral to the configuration space path integral, a nontrivial contribution to the measure arises that is not manifestly covariant and which is not simply due to the presence of second-class constraints.