Abelian Vector Field Research Articles

STATISTICAL ANISOTROPY AND THE VECTOR CURVATON PARADIGM

The vector curvaton paradigm is reviewed. The mechanism allows a massive vector boson field to contribute to or even generate the curvature perturbation in the Universe. Contribution of vector bosons is likely to generate statistical anisotropy in the spectrum and bispectrum of the curvature perturbation, which will soon be probed observationally. Two specific models for the generation of superhorizon spectra for the components of an Abelian vector field are analyzed. Emphasis is put on the observational signatures of the models when the vector fields play the role of vector curvatons. If future observations support the vector curvaton mechanism this will open a window into the gauge field content of theories beyond the standard model.

Lorentz-violating alternative to the Higgs mechanism?

We consider a four-dimensional field-theory model with two massless fermions, coupled to an Abelian vector field without flavour mixing, and to another Abelian vector field with flavour mixing. Both Abelian vectors have a Lorentz-violating kinetic term, introducing a Lorentz-violation mass scale $M$, from which fermions and the flavour-mixing vector get their dynamical masses, whereas the vector coupled without flavour mixing remains massless. When the two coupling constants have similar values in order of magnitude, a mass hierarchy pattern emerges, in which one fermion is very light compared to the other, whilst the vector mass is larger than the mass of the heavy fermion. The work presented here may be considered as a Lorentz-symmetry-Violating alternative to the Higgs mechanism, in the sense that no scalar particle (fundamental or composite) is necessary for the generation of the vector-meson mass. However, the model is not realistic given that, as a result of Lorentz Violation, the maximal (light-cone) speed seen by the fermions is smaller than that of the massless gauge boson (which equals the speed of light in vacuo) by an amount which is unacceptably large to be compatible with the current tests of Lorentz Invariance, unless the gauge couplings assume unnaturally small values. Possible ways out of this phenomenological drawback are briefly discussed, postponing a detailed construction of more realistic models for future work.

Actions for non-abelian twisted self-duality

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms together with their duals and is manifestly duality invariant. Space–time covariance is no longer manifest but still present with a non-standard realization of space–time diffeomorphisms on the gauge fields. In this paper, we give a non-abelian generalization of this first-order action by gauging part of its global symmetries. The resulting field equations are non-abelian versions of the twisted self-duality equations. A key element in the construction is the introduction of proper couplings to higher-rank tensor fields. We discuss possible applications (to Yang–Mills and supergravity theories) and comment on the relation to previous no-go theorems.

Stückelberg mechanisms for tensor multiplets and compactification onAdS3×S3

We present St\"uckelberg mechanisms for tensor multiplets coupled to supergravity in four dimensions (4D), six dimensions (6D), and three dimensions (3D). For $N=1$ supergravity in 4D, our field content is $(e_{\ensuremath{\mu}}{}^{m},{\ensuremath{\psi}}_{\ensuremath{\mu}})$, $({B}_{\ensuremath{\mu}\ensuremath{\nu}},\ensuremath{\chi},\ensuremath{\varphi})$ and $({A}_{\ensuremath{\mu}},\ensuremath{\lambda})$, respectively, for the supergravity, tensor, and vector multiplets. In our St\"uckelberg mechanism, the Abelian vector field ${A}_{\ensuremath{\mu}}$ is absorbed into the longitudinal component of the tensor ${B}_{\ensuremath{\mu}\ensuremath{\nu}}$, which becomes massive. The field strength $F=dA$ of $A$ is replaced by $\mathcal{F}\ensuremath{\equiv}F+mB$, where $m$ is a coupling constant with the dimension of mass. In 6D, we utilize the so-called dual version for $N=2$ supergravity, in order to avoid the obstruction caused by the Chern-Simons term $F\ensuremath{\wedge}A$ in the $B$-field strength $G$. Instead of the $F\ensuremath{\wedge}A$-term in $G$, the 6D Lagrangian has a peculiar topological and cubic interaction term proportional to ${m}^{\ensuremath{-}1}\mathcal{F}\ensuremath{\wedge}\mathcal{F}\ensuremath{\wedge}\mathcal{F}$. In 3D, we also show that a similar mechanism works for $N=1$ supergravity. Interestingly, the basic structure is parallel to the 4D case, except that the originally nonpropagating field $B$ starts propagating, after absorbing the $A$-field. We also show a possible compactification of 6D theory on ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{3}$.

Vector curvaton with varying kinetic function

A new model realisation of the vector curvaton paradigm is presented and analysed. The model consists of a single massive Abelian vector field, with a Maxwell type kinetic term. By assuming that the kinetic function and the mass of the vector field are appropriately varying during inflation, it is shown that a scale invariant spectrum of superhorizon perturbations can be generated. These perturbations can contribute to the curvature perturbation of the Universe. If the vector field remains light at the end of inflation it is found that it can generate substantial statistical anisotropy in the spectrum and bispectrum of the curvature perturbation. In this case the non-Gaussianity in the curvature perturbation is predominantly anisotropic, which will be a testable prediction in the near future. If, on the other hand, the vector field is heavy at the end of inflation then it is demonstrated that particle production is approximately isotropic and the vector field alone can give rise to the curvature perturbation, without directly involving any fundamental scalar field. The parameter space for both possibilities is shown to be substantial. Finally, toy-models are presented which show that the desired variation of the mass and kinetic function of the vector field can be realistically obtained, without unnatural tunings, in the context of supergravity or superstrings.

Gravitating opposites attract

Generalizing previous work by two of the authors, we prove the non-existence of certain stationary configurations in general relativity having a spatial reflection symmetry across a non-compact surface disjoint from the matter region. Our results cover cases such as that of two symmetrically arranged rotating bodies with anti-aligned spins in n + 1 (n ⩾ 3) dimensions, or two symmetrically arranged static bodies with opposite charges in (3 + 1) dimensions. They also cover certain symmetric configurations in (3 + 1)-dimensional gravity coupled to a collection of scalars and Abelian vector fields, such as those that arise in supergravity and Kaluza–Klein models. We also treat the bosonic sector of simple supergravity in 4 + 1 dimensions.

Deformations of Maxwell algebra and their dynamical realizations

We study all possible deformations of the Maxwell algebra. In D = d+1≠3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)⊕so(d,1) or to so(d,2)⊕so(d,1) depending on the signs of the deformation parameter. We construct in the dS(AdS) space a model of massive particle interacting with Abelian vector field via non-local Lorentz force. In D = 2+1 the deformations depend on two parameters b and k. We construct a phase diagram, with two parts of the (b,k) plane with so(3,1)⊕so(2,1) and so(2,2)⊕so(2,1) algebras separated by a critical curve along which the algebra is isomorphic to Iso(2,1)⊕so(2,1). We introduce in D = 2+1 the Volkov-Akulov type model for a Abelian Goldstone-Nambu vector field described by a non-linear action containing as its bilinear term the free Chern-Simons Lagrangean.

Improved generating technique forD=5supergravities and squashed Kaluza-Klein black holes

Recently we suggested a solution-generating technique for five-dimensional supergravity with three Abelian vector fields based on the hidden $SO(4,4)$ symmetry of the three-dimensionally reduced theory. This technique generalizes the ${G}_{2(2)}$ generating technique developed earlier for minimal five-dimensional supergravity (A. Bouchareb, G. Cl\'ement, C-M. Chen, D. V. Gal'tsov, N. G. Scherbluk, and Th. Wolf, Phys. Rev. D 76, 104032 (2007)) and provides a new matrix representation for cosets forming the corresponding sigma-models in both cases. Here we further improve these methods introducing a matrix-valued dualization procedure which helps to avoid difficulties associated with solving the dualization equations in the component form. This new approach is used to generate a five-parametric rotating charged Kaluza-Klein black hole with the squashed horizon adding one parameter more to the recent solution by Tomizawa, Yasui, and Morisawa, which was constructed using the previous version of the ${G}_{2(2)}$ generating technique.

Black Holes and Nonrelativistic Quantum Systems

We describe black holes in d+3 dimensions, whose thermodynamic properties correspond to those of a scale-invariant nonrelativistic (d+1)-dimensional quantum system with a dynamical exponent z=2. The gravitational model involves a massive Abelian vector field and a scalar field, in addition to the metric. The energy per particle in the dual theory is |micro|d/(d+2) at any temperature (micro is the chemical potential). The ratio of shear viscosity to entropy density is variant Planck's over 2pi/4pi in any dimension d > or =2.

The end of thep-form hierarchy

The introduction of a non-abelian gauge group embedded into the rigid symmetry group G of a field theory with abelian vector fields and no corresponding charges, requires in general the presence of a hierarchy of p-form gauge fields. The full gauge algebra of this hierarchy can be defined independently of a specific theory and is encoded in the embedding tensor that determines the gauge group. When applied to specific Lagrangians, the algebra is deformed in an intricate way and in general will only close up to equations of motion. The group-theoretical structure of the hierarchy exhibits many interesting features, which have been studied starting from the low-p forms. Here the question is addressed what happens generically for high values of p. In addition a number of other features is discussed concerning the role that the p-forms play in various deformations of the theory.

No cross-interactions among different tensor fields with the mixed symmetry (3, 1) intermediated by a vector field

Under the hypotheses of analyticity in the coupling constant, locality, Lorentz covariance and Poincaré invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a collection of free massless tensor gauge fields with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field, respectively a p-form gauge field, are addressed. The main result is that a single mixed-symmetry tensor field from the collection gets coupled to the vector field/p-form. Our final result resembles the well-known fact from general relativity according to which there is one graviton in a given world.

1/Nccorrections to the magnetic susceptibility of the QCD vacuum

We investigate the magnetic susceptibility of the QCD vacuum with the $1/{N}_{c}$ corrections taken into account, based on the instanton vacuum. Starting from the instanton liquid model, we derive the gauged light-quark partition function in the presence of the current quark mass as well as of external Abelian vector and tensor fields. We consider the $1/{N}_{c}$ meson-loop corrections which are shown to contribute to the magnetic susceptibility by around 15% for the up (and down) quarks. We also take into account the tensor terms of the quark-quark interaction from the instanton vacuum as well as the finite-width effects, both of which are of order $\mathcal{O}(1/{N}_{c})$. The effects of the tensor terms and finite width turn out to be negligibly small. The final results for the up-quarks are given as: $\ensuremath{\chi}⟨i{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\psi}{⟩}_{0}\ensuremath{\simeq}35--40\text{ }\text{ }\mathrm{MeV}$ with the quark condensate $⟨i{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\psi}{⟩}_{0}$. We also discuss the pion mass dependence of the magnetic susceptibility in order to give a qualitative guideline for the chiral extrapolation of lattice data.

Supergravity inspired vector curvaton

It is investigated whether a massive Abelian vector field, whose gauge kinetic function is growing during inflation, can be responsible for the generation of the curvature perturbation in the Universe. Particle production is studied and it is shown that the vector field can obtain a scale-invariant superhorizon spectrum of perturbations with a reasonable choice of kinetic function. After inflation the vector field begins coherent oscillations, during which it corresponds to pressureless isotropic matter. When the vector field dominates the Universe, its perturbations give rise to the observed curvature perturbation following the curvaton scenario. It is found that this is possible if, after the end of inflation, the mass of the vector field increases at a phase transition at temperature of order 1 TeV or lower. Inhomogeneous reheating, whereby the vector field modulates the decay rate of the inflaton, is also studied.

Dynamics of (SUSY) AdS space isometry breaking

Actions governing the dynamics of the Nambu–Goldstone modes resulting from the spontaneous breaking of the SO(4, 2) and SU(2, 2|1) isometries of five-dimensional anti-de Sitter space (AdS5) and SUSY AdS5 × S1 spaces, respectively, due to a restriction of the motion to embedded four-dimensional AdS4 space and four-dimensional Minkowski space (M4) probe branes are presented. The dilatonic Nambu–Goldstone mode governing the motion of the M4 space probe brane into the covolume of the SUSY AdS5 × S1 space is found to be unstable. No such instability appears in the other cases. Gauging these symmetries leads to an Einstein–Hilbert action containing, in addition to the gravitational vierbein, a massive Abelian vector field coupled to gravity.

Couplings between a single massless tensor field with the mixed symmetry (3,1) and one vector field

Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincar\'e invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a single free massless tensor gauge field with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field have been investigated. The computations are done with the help of the deformation theory based on a cohomological approach, in the context of the antifield-BRST formalism. The main result is that there exist nontrivial cross-couplings between these types of fields in five spatiotemporal dimensions, which break the PT invariance and allow for the deformation of the gauge transformations of the vector field, but not of the gauge algebra.

Nonlinear realization of local symmetries of AdS space

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local symmetries of $Ad{S}_{d+1}$ space due to the embedding of an $Ad{S}_{d}$ brane. The resulting action is an $SO(2,d)$ invariant $AdS$ form of the Einstein-Hilbert action, which in addition to the $Ad{S}_{d}$ gravitational vielbein, also includes a massive vector field localized on the brane. Its long wavelength dynamics is the same as a massive Abelian vector field coupled to gravity in $Ad{S}_{d}$ space.

The holographic mapping of the standard model onto the black hole horizon: I. Abelian vector field, scalar field and BEH mechanism

Interactions between outgoing Hawking particles and ingoing matter are determined by gravitational forces and standard model interactions. In particular, the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the standard model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon's dynamics. The relation between ingoing and outgoing states is described in terms of an operator algebra. In this paper, the first of a series, we describe the algebra induced on the horizon by U(1) vector fields and scalar fields, including the case of an Englert–Brout–Higgs mechanism, and a more careful consideration of the transverse vector field components.

Magnetic susceptibility of the QCD vacuum

We investigate the magnetic susceptibility of the QCD vacuum, based on the instanton vacuum. Starting from the instanton liquid model for the instanton vacuum, we derive the light-quark partition function Z[V,T,mˆ] in the presence of the current quark mass mˆ as well as the external Abelian vector and tensor fields. We calculate a two-point correlation function relevant for the magnetic susceptibility and derive it beyond the chiral limit. We obtain for the different flavors the following magnetic susceptibility: χu,d〈iψu,d†ψu,d〉0∼40–45MeV, while χs〈iψs†ψs〉0≃6–10MeV with the quark condensate 〈iψ†ψ〉0.

Abelian and nonabelian vector field effective actions from string field theory

The leading terms in the tree-level effective action for the massless fields of the bosonic open string are calculated by integrating out all massive fields in Witten's cubic string field theory. In both the abelian and nonabelian theories, field redefinitions make it possible to express the effective action in terms of the conventional field strength. The resulting actions reproduce the leading terms in the abelian and nonabelian Born-Infeld theories, and include (covariant) derivative corrections.

Interacting fermions and domain wall defects in 2+1 dimensions

We consider a Dirac field in 2+1 dimensions with a domain wall like defect in its mass, minimally coupled to a dynamical Abelian vector field. The mass of the fermionic field is assumed to have just one linear domain wall, which is externally fixed and unaffected by the dynamics. We show that, under some general conditions on the parameters, the localized zero modes predicted by the Callan and Harvey mechanism are stable under the electromagnetic interaction of the fermions.