Antisymmetric Tensor Field Research Articles

Antisymmetric tensor generalizations of affine vector fields.

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank-p antisymmetric affine tensor fields in n-dimensions is bounded by (n + 1)!/p!(n - p)!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

Coupling of Hidden Sector

A hypothetic Hidden Sector of the Universe, consisting of sterile fermions ("sterinos") and sterile mediating bosons ("sterons") of mass dimension 1 (not 2!) - the last described by an antisymmetric tensor field - requires to exist also a scalar isovector and scalar isoscalar in order to be able to construct electroweak invariant coupling (before spontaneously breaking its symmetry).

Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux

We consider six-dimensional supergravity compactified on orbifolds with Wilson lines and bulk flux. Torus Wilson lines are decomposed into Wilson lines around the orbifold fixed points, and twisted boundary conditions of matter fields are related to fractional localized flux. Both, orbifold singularities and flux lead to chiral fermions in four dimensions. We show that in addition to the standard bulk and fixed point anomalies the Green-Schwarz term also cancels the four-dimensional anomaly induced by the flux background. The two axions contained in the antisymmetric tensor field both contribute to the cancellation of the four-dimensional anomaly and the generation of a vector boson mass via the Stueckelberg mechanism. An orthogonal linear combination of the axions remains massless and couples to the gauge field in the standard way. Furthermore, we construct convenient expressions for the wave functions of the zero modes and relate their multiplicity and behavior at the fixed points to the bulk flux quanta and the Wilson lines.

Observations on BI from N = 2 $$ \mathcal{N}=2 $$ supergravity and the general Ward identity

The multi-vector generalization of a rigid, partially-broken $$ \mathcal{N}=2 $$ supersymmetric theory is presented as a rigid limit of a suitable gauged $$ \mathcal{N}=2 $$ supergravity with electric, magnetic charges and antisymmetric tensor fields. This on the one hand generalizes a known result by Ferrara, Girardello and Porrati while on the other hand allows to recover the multi-vector BI models of [4] from $$ \mathcal{N}=2 $$ supergravity as the end-point of a hierarchical limit in which the Planck mass first and then the supersymmetry breaking scale are sent to infinity. We define, in the parent supergravity model, a new symplectic frame in which, in the rigid limit, manifest symplectic invariance is preserved and the electric and magnetic Fayet-Iliopoulos terms are fully originated from the dyonic components of the embedding tensor. The supergravity origin of several features of the resulting rigid supersymmetric theory are then elucidated, such as the presence of a traceless SU(2)- Lie algebra term in the Ward identity and the existence of a central charge in the supersymmetry algebra which manifests itself as a harmless gauge transformation on the gauge vectors of the rigid theory; we show that this effect can be interpreted as a kind of “superspace non-locality” which does not affect the rigid theory on space-time. To set the stage of our analysis we take the opportunity in this paper to provide and prove the relevant identities of the most general dyonic gauging of Special-Kaehler and Quaternionic-Kaehler isometries in a generic $$ \mathcal{N}=2 $$ model, which include the supersymmetry Ward identity, in a fully symplectic-covariant formalism.

On the possibility of tree-level leptogenesis from Kalb-Ramond torsion background.

In this work we consider a phenomenological model for leptogenesis in the context of a Standard Model Extension with an axial-like background coupling to fermions that violates both Lorentz and CPT symmetries. The latter is motivated by a background geometry of the early Universe involving a particular kind of torsion, arising from the Kalb–Ramond antisymmetric tensor field which appears in the gravitational multiplet of string theory, although we do not restrict ourselves to this framework. It is shown that leptogenesis can occur even at tree level and with only one generation of right-handed heavy Majorana neutrinos, due to { CP } and CPT violation introduced by the background geometry. Important issues for the model, including (a) its compatibility with a conventional-like cosmology and (b) current-era phenomenology (characterised by very stringent bounds on the allowed amount of torsion) are pointed out, and potential ways of resolving them, within the framework of string-theory models, are discussed.

Antisymmetric tensor field and spontaneous magnetization in holographic duality

A real anti-symmetric tensor field was introduced to realize a holographic magnetic ordered phase in our previous works. However, a more careful analysis shows there is a vector ghost in the model. In this paper we present a modified Lagrangian density for the anti-symmetric tensor, which is ghost free and causality is well-defined, and keeps all the significant results in the original model qualitatively. We show this modified Lagrangian density could come from the dimensional compactification of $p$-form field in String/M-theory. For static curved space-time, we also prove that this modified model is ghost free and dose not violate causality. This new model offers a solid foundation for the application of antisymmetric tensor field in holographic duality, especially for the spontaneous magnetization.

Scattering of stringy states in compactified closed bosonic string

We present scattering of stringy states of closed bosonic string compactified on torus Td. We focus our attention on scattering of moduli and gauge bosons. These states appear when massless excitations such as graviton and antisymmetric tensor field of the uncompactified theory are dimensionally reduced to lower dimension. The toroidally compactified theory is endowed with the T-duality symmetry, O(d,d). Therefore, it is expected that the amplitude for scattering of such states will be T-duality invariant. The formalism of Kawai–Lewellen–Tye is adopted and appropriately tailored to construct the vertex operators of moduli and gauge bosons. It is shown, in our approach, that N-point amplitude is T-duality invariant. We present illustrative examples for the four point amplitude to explicitly demonstrate the economy of our formalism when three spatial dimensions are compactified on T3. It is also shown that if we construct an amplitude with a set of ‘initial’ backgrounds, the T-duality operation transforms it to an amplitude associated with another set backgrounds. We propose a modified version of KLT approach to construct vertex operators for nonabelian massless gauge bosons which appear in certain compactification schemes.

Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

Recently, several discussions on the possible observability of 4-vector potential have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 electromagnetic field. We re-examine the theory of antisymmetric tensor field and 4-vector potentials. We study the massless limits too. In fact, a theoretical motivation for this venture is old papers of Ogievetskii and Polubarinov, Hayashi, and Kalb and Ramond, which are widely accepted by physics community. This paper is based on two poster presentations About the Longitudinal Nature of the Antisymmetric Tensor Field after Quantization and Normalization and m->0 Limit of the Proca Theory at the Workshop Lorentz Group, CPT and Neutrinos (Zacatecas, Mexico, June 23-26, 1999).

Formula omitted] symmetry breaking by rank three and rank two antisymmetric tensor scalars

We study SU(n) symmetry breaking by rank three and rank two antisymmetric tensor fields. Using tensor analysis, we derive branching rules for the adjoint and antisymmetric tensor representations, and explain why for general SU(n) one finds the same U(1) generator mismatch that we noted earlier in special cases. We then compute the masses of the various scalar fields in the branching expansion, in terms of parameters of the general renormalizable potential for the antisymmetric tensor fields.

Holographic model for the paramagnetism/antiferromagnetism phase transition

In this paper we build a holographic model of paramagnetism/antiferromagnetism phase transition, which is realized by introducing two real antisymmetric tensor fields coupling to the background gauge field strength and interacting with each other in a dyonic black brane background. In the case without external magnetic field and in low temperatures, the magnetic moments condense spontaneously in antiparallel manner with the same magnitude and the time reversal symmetry is also broken spontaneously (if boundary spatial dimension is more than 2, spatial rotational symmetry is broken spontaneously as well), which leads to an antiferromagnetic phase. In the case with weak external magnetic field, the magnetic susceptibility density has a peak at the critical temperature and satisfies the Curie-Weiss law in the paramagnetic phase of antiferromagnetism. In the strong external magnetic field case, there is a critical magnetic field $B_c$ in antiferromagnetic phase: when magnetic field reaches $B_c$, the system will return into the paramagnetic phase by a second order phase transition.

Heavy WIMP through Higgs portal at the LHC

The LHC constraints on Higgs-portal WIMPs are studied. Scalar, vector and anti-symmetric tensor fields are considered. They are assumed to be heavier than a half of the Higgs boson mass. We investigate 8 TeV LHC results on signatures of the vector boson fusion, mono-jet and associated production of the Z boson, which proceed via virtual exchange of the Higgs boson. We show that the vector boson fusion channel gives the most stringent constraints on Higgs-portal interactions for all the WIMP models investigated here. The upper limits on vector and tensor Higgs-portal couplings can be 0.43 and 0.16 for the WIMP mass of 65 GeV, respectively. However, they are rapidly weakened for heavier WIMP masses, allowing O(1) couplings for masses heavier than ∼100 GeV. Constraints for scalar WIMPs are very weak. Prospects of the 14 TeV LHC are also discussed. We show that the constraints on the tensor and vector couplings would be improved by a factor of ∼1.5–2, depending on the search channels. It would be still challenging to constrain scalar WIMPs.

Notoph-Graviton-Photon Coupling

In the sixties Ogievetskii and Polubarinov proposed the concept of notoph, whose helicity properties are complementary to those of photon. Later, Kalb and Ramond (and others) developed this theoretical concept. And, at the present times it is widely accepted. We analyze the quantum theory of antisymmetric tensor fields with taking into account mass dimensions of notoph and photon. It appears to be possible the description of both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor.Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it, and we obtain the spin-2 relativistic equations, which are consistent with the general relativity. The importance of the 4-vector field (and its gauge part) is pointed out.Thus, we present the full theory which contains the photon, the notoph (the Kalb-Ramond field) and the graviton. The relations of this theory with the higher spin theories are established. In fact, we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with scalar-tensor theories of gravitation and f(R) are discussed. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they will be probably seen in experiments in the next few years.

Why has spacetime torsion such negligible effect on the Universe?

We attempt an answer to the question as to why the evolution of a four-dimensional universe is governed by spacetime curvature but not torsion. An answer is found if there is an additional compact spacelike dimension with a warped geometry, with torsion caused by a Kalb-Ramond (KR) antisymmetric tensor field in the bulk. Starting from a Randall-Sundrum type of warped extra dimension, and including the inevitable backreaction ensuing from the radius stabilization mechanism, we show that there is always an extra exponential suppression of the KR field on the four-dimensional projection that constitutes our visible Universe. The backreaction is found to facilitate the process of such suppression.

Finite BRST–antiBRST transformations in Lagrangian formalism

We continue the study of finite BRST–antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λa, a=1,2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λa. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31]) for finite field-dependent BRST–antiBRST transformations with functionally-dependent parameters, λa=saΛ, induced by a finite even-valued functional Λ(ϕ,π,λ) and by the generators sa of BRST–antiBRST transformations, acting in the space of fields ϕ, antifields ϕa⁎,ϕ¯ and auxiliary variables πa,λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λa, and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of a non-Abelian antisymmetric tensor field.

Paramagnetism-ferromagnetism phase transition in a dyonic black hole

Coupling an antisymmetric tensor field to the electromagnetic field in a dyonic Reissner-Nordstr\"om-anti--de Sitter black hole background, we build a holographic model for the paramagnetism/ferromagnetism phase transition. In the case of zero magnetic field, the time reversal symmetry is broken spontaneously and spontaneous magnetization happens at low temperatures. The critical exponents are in agreement with the ones from mean field theory. In the case of nonzero magnetic field, the model realizes the hysteresis loop of a single magnetic domain and the magnetic susceptibility satisfies the Curie-Weiss law.

Dark matter stability without new symmetries

The stability of dark matter is normally achieved by imposing extra symmetries beyond those of the Standard Model of Particle Physics. In this paper we present a framework where the dark matter stability emerges as a consequence of the Standard Model symmetries. The dark matter particle is an antisymmetric tensor field (analogous to the one used for spin-1 mesons in QCD), singlet under the Standard Model gauge group. The Lagrangian possesses an accidental $Z_2$ symmetry which makes the dark matter stable on cosmological time scales. Interactions with the Standard Model fields proceed through the Higgs portal, which allows the observed dark matter abundance to be generated via thermal freeze-out. We also discuss the prospects for observing this dark matter particle in direct detection experiments.

Notoph-Graviton-Photon Coupling in the Minkowski Space

Ogievetskii and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum theory of antisymmetric tensor fields with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with scalar-tensor theories of gravitation and f(R) are discussed. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and conclude that they will be probably seen in experiments in the next few years.

Treatment of a system with explicitly broken gauge symmetries

A system in which the free part of the action possesses a gauge symmetry that is not respected by the interacting part presents problems when quantized. We illustrate how the Dirac constraint formalism can be used to address this difficulty by considering an antisymmetric tensor field interacting with a spinor field.

Rotating and moving D-branes in the presence of various background fields

We calculate the bosonic boundary state associated with a rotating and moving $\mathrm{D}p$-brane in the presence of the antisymmetric tensor field, a $U(1)$ gauge field and a tachyon field. Rotation and motion are in the brane volume. We reconstruct this boundary state via the group $PSL(2,R)$ to be applicable when the tachyon field is presented. This modified boundary state enables us to calculate the interaction amplitude between two parallel $\mathrm{D}p$-branes with rotation and motion. The long-range force of this interaction will be obtained. The boundary state also enables us to investigate the tachyon condensation on a rotating and moving $\mathrm{D}p$-brane.

Low-lying pseudoscalar and vector mesons and their dynamics

In chiral perturbation theory, the leading-order contribution to reactions with pions in the sector of odd intrinsic parity is defined by the Wess-Zumino-Witten structure. This structure is supplemented by a simple vector-meson Lagrangian where the vector mesons are described by antisymmetric tensor fields. With the rho-omega-pion coupling as the only parameter in the sector of odd intrinsic parity, i.e. without additional contact terms, one can achieve a proper description of the single- and double-virtual pion transition form factor and the three-pion production in electron-positron collisions.