Rank Antisymmetric Tensor Field Research Articles

Gravitational waves from inflation with antisymmetric tensor field

We build upon the past studies of inflation with rank-2 antisymmetric tensor field, including here the tensor perturbations to metric. We perform a comprehensive analysis of the background dynamics of our model in the presence of non-minimal coupling curvature terms R and Rμ ν. We find appropriate conditions on the nonminimal coupling parameters to satisfy the constraint of speed of propagation of gravitational waves. Including the tensor perturbations, the model is found to be free from ghost instabilities with minimal constraints on the parameters. We also study the evolution of gravitational waves, calculate the power spectrum and the tensor spectral index.

Scalaron tunneling and the fate of antisymmetric tensor fields in F(R) gravity

The work provides a possible explanation of a well motivated question—why the present Universe is practically free from any noticeable footmarks of higher rank antisymmetric tensor fields, despite having the signatures of scalar, vector, fermion as well as symmetric rank 2 tensor field in the form of gravity? The explanation proposed here originates from the higher curvature degrees of freedom present in a F(R) gravity model. In such a model, we show that the scalar degree of freedom (also known as scalaron) associated with the higher curvature term may undergo a quantum tunneling which in turn suppresses the couplings of antisymmetric massless tensor fields with various standard model fields.

Cosmological quantum entanglement: a possible testbed for the existence of Kalb–Ramond field

In the present paper, we explore the possible effects of a second rank antisymmetric tensor field, known as Kalb–Ramond (KR) field, on cosmological particle production as well as on quantum entanglement for a massive scalar field propagating in a four dimensional FRW spacetime evolves through a symmetric bounce. For this purpose, the scalar field is considered to be coupled with the KR field and also with the Ricci scalar via the term ∼ξRΦ2 (with ξ be the coupling). The presence of KR field spoils the conformal symmetry of a massless scalar field even for ξ = 1/6 in four dimensional context, which has interesting consequences on particle production and consequently on quantum entanglement as we will discuss. In particular, the presence of KR field in an FRW bouncing Universe allows a greater particle production and consequently the upper bound of the entanglement entropy becomes larger in comparison to the case when the KR field is absent. This may provide an interesting testbed for the existence of Kalb–Ramond field in our Universe.

Lorentz-violating gaugeon formalism for rank-2 tensor theory

We develop a BRST symmetric gaugeon formalism for the Abelian rank-2 antisymmetric tensor field in the Lorentz-breaking framework. The Lorentz-breaking is achieved here by considering a proper subgroup of Lorentz group together with translation. In this scenario, the gaugeon fields together with the standard fields of the Abelian rank-2 antisymmetric tensor theory get mass. In order to develop the gaugeon formulation for this theory in very special relativity (VSR), we first introduce a set of dipole vector fields as a quantum gauge freedom to the action. In order to quantize the dipole vector fields, the VSR-modified gauge-fixing and corresponding ghost action are constructed as the classical action is invariant under a VSR-modified gauge transformation. Further, we present a Type I gaugeon formalism for the Abelian rank-2 antisymmetric tensor field theory in VSR. The gauge structures of Fock space constructed with the help of BRST charges are also discussed.

The anomalous U(1)_{mathrm{anom}}\xa0 symmetry and flavors from an SU(5) times SU(5)' GUT in mathbf{Z}_{12-I} orbifold compactification

In string compactifications, frequently the anomalous U(1) gauge symmetry appears which belongs to E_8 times E_8' of the heterotic string. This anomalous U(1) gauge boson obtains mass at the compactification scale (approx 10^{18,},text {GeV}) by absorbing one pseudoscalar (corresponding to the model-independent axion) from the second rank antisymmetric tensor field B_{MN}. Below the compactification scale a global symmetry U(1)_{mathrm{anom}} results whose charge Q_mathrm{anom} is the original gauge U(1) charge. This is the most natural global symmetry, realizing the “invisible” axion. This global symmetry U(1)_{mathrm{anom}} is suitable for a flavor symmetry. In the simplest compactification model with the flipped SU(5) grand unification, all the low energy parameters are calculated in terms of the vacuum expectation values of the standard model singlets.

Higher rank antisymmetric tensor fields in Klebanov-Strassler geometry

In string theory, higher rank antisymmetric tensor fields appear as massless excitations of closed strings. Till date there is no experimental support in favour of their existence. In a stringy framework, starting from a warped throat-like Klebanov-Strassler geometry, we show that all the massless higher rank antisymmetric tensor fields are heavily suppressed due to the background fluxes leading to their invisibility in our Universe.

All the fundamental massless bosonic fields in superstring theory

AbstractA systematic analysis of all the massless bosonic fields in superstring theory is carried out. Emphasis is put on the derivation of their propagators, their polarization aspects and the investigation of their underlying constraints as well as their number of degrees of freedom. The treatment is given in the presence of external sources, in the celebrated Coulomb gauge, ensuring the positivity of the formalism ‐ a result which is also established in the process. The challenge here is the investigation involved in the self‐dual fourth rank anti‐symmetric tensor field. No constraints are imposed on the external sources so that their components may be varied independently, thus the complete expressions of the propagators may be obtained. As emphasized in our earlier work, the latter condition is an important one in dynamical theories with constraints giving rise to modifications as Faddeev‐Popov factors. The analysis is carried out in 10 dimensions, not only because of the consistency requirement by the superstrings, but also in order to take into account of the self‐duality character of the fourth rank anti‐symmetric tensor field as spelled out in the paper.

Theory and phenomenology of spin-1 chiral particles

We consider all possible finite representations of the Lorentz group and their association with the spin properties of the particles. It is shown that, for a given nontrivial spin, there exist several nonequivalent representations differing in chirality, which in the massless case correspond to different particles with different helicities. A spin-1 case, which includes the standard field description by the vector-potential and a non-standard one by the second rank antisymmetric tensor field, is considered in detail. The first field transforms under the real representation (1/2,1/2), while the second one does so under the chiral representations (1,0) and (0,1). By considering spin-1 hadron resonances as an example, it is shown that these two fields describe two different types of particles existing in nature. This idea is further applied to the construction of the Standard Model extension using a new type of spin-1 chiral particles. Its phenomenological consequences are studied in detail.

Integrability of the symmetry reduced bosonic dynamics and soliton generating transformations in the low energy heterotic string effective theory

Integrable structure of the symmetry reduced dynamics of massless bosonic sector of the heterotic string effective action is presented. For string background equations that govern in the space-time of D dimensions (D ≥ 4), the dynamics of interacting gravitational, dilaton, antisymmetric tensor and any number n ≥ 0 of Abelian vector gauge fields, all depending only on two coordinates, we construct an equivalent (2d + n) × (2d + n)-matrix spectral problem (d = D ― 2). This spectral problem provides the base for the development of various solution constructing procedures (dressing transformations, integral equation methods). For the case of the absence of Abelian gauge fields, we present the soliton generating transformations of any background with interacting gravitational, dilaton, and the second rank antisymmetric tensor fields.

CHIRAL FREEDOM AND THE SCALE OF WEAK INTERACTIONS

A second rank antisymmetric tensor field is proposed as an alternative to the Higgs scalar. No mass term is allowed by the symmetries. At the scale where the asymptotically free chiral couplings of the fermions grow large, condensates of top–antitop and bottom–antibottom may induce the spontaneous breaking of the electroweak gauge symmetry. This would solve the gauge hierarchy problem by dimensional transmutation, similar to QCD.

Gauge invariant Lagrangian construction for massive bosonic mixed symmetry higher spin fields

We develop the BRST approach to gauge invariant Lagrangian construction for the massive mixed symmetry integer higher spin fields described by the rank-two Young tableaux in arbitrary dimensional Minkowski space. The theory is formulated in terms of auxiliary Fock space. No off-shell constraints on the fields and the gauge parameters are imposed. The approach under consideration automatically leads to a gauge invariant Lagrangian for massive theory with all appropriate Stückelberg fields. It is shown that all the restrictions defining an irreducible representation of the Poincaré group arise from Lagrangian formulation as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive the gauge-invariant Lagrangian for massive rank-2 antisymmetric tensor field containing the complete set of auxiliary fields and gauge parameters.

Signature reversal invariance

We consider the signature reversing transformation of the metric tensor g μ ν → − g μ ν induced by the chiral transformation of the curved space gamma matrices γ μ → γ γ μ in spacetimes with signature ( S , T ) , which also induces a ( − 1 ) T spacetime orientation reversal. We conclude: (1) It is a symmetry only for chiral theories with S − T = 4 k , with k integer. (2) Yang–Mills theories require dimensions D = 4 k with T even for which even rank antisymmetric tensor field strengths and mass terms are also allowed. For example, D = 10 super-Yang–Mills is ruled out. (3) Gravitational theories require dimensions D = 4 k + 2 with T odd, for which the symmetry is preserved by coupling to odd rank field strengths. In D = 10 , for example, it is a symmetry of N = 1 and type IIB supergravity but not type IIA. A cosmological term and also mass terms are forbidden but non-minimal R ϕ 2 coupling is permitted. (4) Spontaneous compactification from D = 4 k + 2 leads to interesting but different symmetries in lower dimensions such as D = 4 , so Yang–Mills terms, Kaluza–Klein masses and a cosmological constant may then appear. As a well-known example, IIB permits AdS 5 × S 5 .

Worldline approach to vector and antisymmetric tensor fields II

We extend the worldline description of vector and antisymmetric tensor fields coupled to gravity to the massive case. In particular, we derive a worldline path integral representation for the one-loop effective action of a massive antisymmetric tensor field of rank p (a massive p-form) whose dynamics is dictated by a standard Proca-like lagrangian coupled to a background metric. This effective action can be computed in a proper time expansion to obtain the corresponding Seeley-DeWitt coefficients a0, a1, a2. The worldline approach immediately shows that these coefficients are derived from the massless ones by the simple shift D -> D+1, where D is the spacetime dimension. Also, the worldline representation makes it simple to derive exact duality relations. Finally, we use such a representation to calculate the one-loop contribution to the graviton self-energy due to both massless and massive antisymmetric tensor fields of arbitrary rank, generalizing results already known for the massless spin 1 field (the photon).

Positivity bounds for the Yano-Arnowitt-Deser-Misner mass density

Killing-Yano tensors are natural generalizations of Killing vectors to arbitrary rank anti-symmetric tensor fields. It was recently shown that Killing-Yano tensors lead to conserved gravitational charges, called Y-ADM charges. These new charges are interesting because they measure, for example, the mass density of a p-brane, rather than the total ADM mass which may be infinite. In this paper, we show that the spinorial techniques used by Witten, in his proof of the positive energy theorem, may be straightforwardly extended to study the positivity properties of the Y-ADM mass density for p-brane spacetimes. Although the resulting formalism is quite similar to the ADM case, we show that establishing a positivity bound in the higher rank Y-ADM case requires imposing a condition on the Weyl tensor in addition to an energy condition. We find appropriate energy conditions for spacetimes that are conformally flat or algebraically special, and for spacetimes that have an exact Killing vector along the brane. Finally we discuss our expression for the Y-ADM mass density from the Hamiltonian point of view.

Geons with spin and charge

We construct new geon-type black holes in D ⩾ 4 dimensions for Einstein's theory coupled to gauge fields. A static non-degenerate vacuum black hole has a geon quotient provided the spatial section admits a suitable discrete isometry, and an antisymmetric tensor field of rank 2 or D − 2 with a pure F2 action can be included by an appropriate (and in most cases non-trivial) choice of the field strength bundle. We find rotating geons as quotients of the Myers–Perry(-AdS) solution when D is odd and not equal to 7. For other D we show that such rotating geons, if they exist at all, cannot be continuously deformed to zero angular momentum. With a negative cosmological constant, we construct geons with angular momenta on a torus at the infinity. As an example of a non-Abelian gauge field, we show that the D = 4 spherically symmetric SU(2) black hole admits a geon version with a trivial gauge bundle. Various generalizations, including both black-brane geons and Yang–Mills theories with Chern–Simons terms, are briefly discussed.

Dimensionality in the Freund–Rubin cosmology

In the n-dimensional Freund–Rubin model with an antisymmetric tensor field of rank s−1, the dimension of the external spacetime we live in must be min(s,n−s). This result is a generalization of the previous result in the d=11 supergravity case, where s=4.

S-brane solutions in supergravity theories

In this paper time dependent solutions of supergravities with dilaton and arbitrary rank antisymmetric tensor field are found. Although the solutions are nonsupersymmetric the equations of motions can be integrated in a simple form. Such supergravity solutions are related to Euclidean or spacelike branes (S-branes).

QUANTIZATION OF MASSIVE ABELIAN ANTISYMMETRIC TENSOR FIELD AND LINEAR POTENTIAL

We discuss a quantum-theoretical aspect of the massive Abelian antisymmetric tensor gauge theory with antisymmetric tensor current. To this end, an Abelian rank-2 antisymmetric tensor field is quantized both in the covariant gauge with an arbitrary gauge parameter and in the axial gauge of the Landau type. The covariant quantization yields the generating functional written in terms of an antisymmetric tensor current and its divergence. Origins of the terms in the generating functional are clearly understood in comparison with the quantization in the unitary gauge. The quantization in the axial gauge with a suitable axis directly yields the generating functional which is the same as that obtained by using Zwanziger's formulation for electric and magnetic charges. It is shown that the generating functionals lead to a composite of the Yukawa and the linear potentials.

Spherically symmetric solutions of gravitational field equations in Kalb–Ramond background

Static spherically symmetric solutions in a background spacetime with torsion is derived explicitly. The solutions are shown to possess interesting features like ‘wormholes’ or ‘naked singularity’ in spacetime. The torsion considered here is identified with the field strength of a second rank antisymmetric tensor field namely the Kalb–Ramond field and the proposed solution therefore has much significance in a string inspired gravitational field theory.

Nonlinear realization of Lorentz symmetry

We explore a nonlinear realization of the (2+1)-dimensional Lorentz symmetry with a constant vacuum expectation value of the second rank anti-symmetric tensor field. By means of the nonlinear realization, we obtain the low-energy effective action of the Nambu–Goldstone bosons for the spontaneous Lorentz symmetry breaking.