Second-rank Antisymmetric Tensor Research Articles

Dynamical Lorentz symmetry breaking in a tensor bumblebee model

In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor, calculate the one-loop effective potential of the (pseudo)tensor field, and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking. We also argue that, contrarily to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined potential and thus do not allow for the dynamical Lorentz symmetry breaking.

Family unification in special grand unification

We discuss family unification in grand unified theory (GUT) based on an $SU(19)$ GUT gauge group broken to its subgroups including a special subgroup. In the $SU(19)$ GUT on the six-dimensional (6D) orbifold space $M^4\times T^2/\mathbb{Z}_2$, three generations of the 4D SM Weyl fermions can be embedded into a 6D bulk Weyl fermions in an $SU(19)$ second-rank anti-symmetric tensor representation. 6D and 4D gauge anomalies can be canceled out by considering proper matter content without 4D exotic chiral fermions at low energies.

A New Action of NC Field Theory with Lorentz Symmetry: -- Application to Gauge Theories --

We propose a new action of non-commutative (NC) field theory with Lorentz symmetry, which is obtained by assuming that the NC parameter transforms like an anti-symmetric second-rank tensor, as in the Doplicher-Fredenhagen-Roberts algebra. It is shown that the new action is formally obtained by deleting the 'explicit' dependence of fields on the NC parameter in the Lorentz-invariant Carlson-Carone-Zobin action without vitiating the applicability of 0-expansion in NC gauge theory and thus is identical to that assumed in a previous paper. This confirms our previous calculations in several field theory models, including Lorentz-invariant spinor NCQED, to formulate NC regularization. The present paper continues the application of this method to scalar NCQED and NC U(N) Yang-Mills with Lorentz symmetry. Considering our previous results, we conclude that the new action can be used to define a quantum field theory on NC space-time, at least in the one-loop approximation, which satisfies the correspondence principle in that it has a smooth commutative limit at the level of Feynman diagrams.

Global Monopole in Kalb–Ramond Background

In recent, S. SenGupta and S. Sur [Phys. Lett. B 502 (2001) 350] have obtained static vacuum solutions of the gravitational field equations in back ground space time with torsion. The torsion is identified with the field strength of a second-rank anti-symmetric tensor field, namely Kalb-Ramond field. In this work, we present the solutions for the metric outside a monopole resulting from the breaking of a global 0(3) symmetry in Kalb-Ramond background. A comparison is made with the corresponding results predicted by general relativity.

Discrete Symmetries in Lorentz-Invariant Non-Commutative QED

It is pointed out that the usual $\theta$-algebra assumed for non-commuting coordinates is not $P$- and $T$-invariant, unless one {\it formally} transforms the non-commutativity parameter $\theta^{\mu\nu}$ in an appropriate way. On the other hand, the Lorentz-covariant DFR algebra, which `relativitizes' the $\theta$-algebra by replacing $\theta^{\mu\nu}$ with a second-rank antisymmetric tensor operator $\htheta^{\mu\nu}$, is $C$-, $ P$- and $T$-invariant. It is then proved that $C, P$ and $T$ are separately conserved in Lorentz-invariant Non-Commutative QED.

The topological B-model with antisymmetric tensor matter fields

A new type of topological matter interactions involving second-rank antisymmetric tensor matter fields with an underlying N T≧1 topological supersymmetry are proposed. The construction of the 4-dimensional, N T =1 super-BF model and the N T =2 topological B-model with tensor matter are explicitly worked out.

Witten's open string field theory in constant B-field background

In this paper we consider Witten's bosonic open string field theory in the presence of a constant background of the second-rank antisymmetric tensor field $B_{ij}$. We extend the operator formulation of Gross and Jevicki in this situation and construct the overlap vertices explicitly. As a result we find a noncommutative structure of the Moyal type only in the zero-mode sector, which is consistent with the result of the correlation functions among vertex operators in the world sheet formulation. Furthermore we find out a certain unitary transformation of the string field which absorbs the Moyal type noncommutative structure. It can be regarded as a microscopic origin of the transformation between the gauge fields in commutative and noncommutative gauge theories discussed by Seiberg and Witten.

ADDENDUM TO “THE RELATIVISTIC COVARIANCE OF THE B-CYCLIC RELATIONS”

In a previous paper [Found. Phys. Lett.10, 383–391 (1997)] we proved that the Evans–Vigier definitions of B(0) and B(3) may be related not with magnetic fields but with a 4-vector field. In the present “Addendum” it is shown that the terms used in the B-cyclic theorem proposed by M. Evans and J.-P. Vigier may have various transformation properties with respect to Lorentz transformations. The fact whether theB(3) field is a part of a bivector (which is equivalent to antisymmetric second-rank tensor) or a part of a 4-vector depends on the phase factors in the definition of positive- and negative-frequency solutions of the (B, E) transverse field. This is closely connected to our considerations of the Bargmann–Wightman–Wigner (Gelfand–Tsetlin–Sokolik) constructs and with Ahluwalia's recent consideration of the phase factor related to gravity. The physical relevance of proposed constructs is discussed.

Space of states of the Freedman-Townsend model in the BLT-quantization scheme

Within the framework of the Lagrangian method of BLT (Batalin-Lavrov-Tyutin) quantization, we have studied the structure of a space of asymptotic states of the well-known Freedman-Townsend model (the model of an antisymmetric second-rank tensor field). We have shown that the physical unitarity condition is satisfied within the considered model.

A Yang–Mills Theory in Loop Space and Chapline–Manton Coupling

We consider a Yang–Mills theory in loop space with the affine gauge group. From this theory, we derive a local field theory with Yang–Mills fields and Abelian antisymmetric and symmetric tensor fields of the second rank. The Chapline–Manton coupling, i.e. coupling of Yang–Mills fields and a second-rank antisymmetric tensor field via the Chern–Simons three-form is obtained systematically.

Couplings of self-dual tensor multiplet in six dimensions

The (1,0) supersymmetry in six dimensions admits a tensor multiplet which contains a second-rank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to a Yang - Mills multiplet, in the absence of supergravity. The self-duality equation for the tensor field involves a Chern - Simons modified field strength, the gauge fermions and an arbitrary dimensionful parameter.

On t-quark decay

An extended electroweak model with second-rank antisymmetric tensor fields was proposed. The effective interactions resulting from the exchange of these fields have a specific dependence on the momentum transfer. This leads to the introduction of new model-independent muon decay parameters (M.V. Chizhov, Mod. Phys. Lett. A 9 (1994) 2979), which can be measured experimentally in SLAC and TRIUMF. The new tensor interactions can affect the three-particle semileptonic meson decays (M.V. Chizhov, Mod. Phys. Lett. A 8 (1993) 2753). In this connection it will be interesting to carry out new experiments on K + → l + νγ, K + → π 0 l + ν decays at DAφNE. The K L-K S mass difference sets constraints to the tensor particles masses. The mass of the lightest tensor particle could be less than the t-quark mass. Therefore, the lightest tensor particle may give an additional W-boson contribution to the t-quark decay with the same signature. In this Letter we have calculated the contribution of the new tensor particles to the t-quark decay.

Quantization of model of antisymmetric tensor field in the framework of extended BRST symmetry

The model of an antisymmetric second-rank tensor field is quantized in both the Lagrangian and the Hamiltonian forms of extended BRST quantization. It is shown that the Lagrangian quantization leads to a unitaryS matrix.

Classical strings subjected to the Lorentz force in loop space.

Interactions of strings with local tensor fields are discussed in terms of the Lorentz force in loop space, the space of all loops in space-time, at the level of classical mechanics. We consider the Nambu-Got\ifmmode \bar{o}\else \={o}\fi{} string interacting with a U(1) gauge field on the loop space and derive a necessary condition to close the algebra that consists of constraints in the system. Examining this condition, we find at the classical level that (a) strings interact with second-rank antisymmetric tensor fields, (b) only tensionless strings interact with massive vector fields in the Stueckelberg formalism, and (c) strings do not interact with massive third-rank tensor fields in a generalized Stueckelberg formalism.

Equations of motion of Dirac-like topological charges in Yang-Mills fields.

Most non-Abelian gauge theories admit the existence of conserved and quantized topological charges as generalizations of the Dirac monopole. Their interactions are dictated by topology. In this paper, previous work in deriving classical equations of motion for these charges is extended to quantized particles described by Dirac wave functions. The resulting equations show intriguing similarities to the Yang-Mills theory. Further, although the system is not dual symmetric, its gauge symmetry is nevertheless doubled as in the Abelian case from {ital G} to {ital G}{times}{ital G}, where the second {ital G} has opposite parity to the first but is mediated instead by an antisymmetric second-rank tensor potential.

LOCAL GAUGE FIELDS BASED ON A U(1) GAUGE THEORY IN LOOP SPACE

We present a U(1) gauge theory defined in loop space, the space of all loops in Minkowski space. On the basis of the U(1) gauge theory, we derive a local field theory of the second-rank antisymmetric tensor field (Kalb-Ramond field) and the Stueckelberg formalism for a massive vector field; the second-rank antisymmetric tensor field and the massive vector field are regarded as parts of a U(1) gauge field on the loop space. We also consider the quantum theories of the second-rank antisymmetric tensor field and the massive vector field on the basis of a BRST formalism for the U(1) gauge theory in loop space. In addition, reparametrization invariance in the U(1) gauge theory is discussed in detail.

Antisymmetric tensor matter fields. An abelian model

We present a simple renormalizable abelian gauge model which includes antisymmetric second-rank tensor fields as matter fields rather than gauge fields known for a long time. The free action is conformally rather than gauge invariant. The quantization of the free fields is analyzed and the one-loop renormalization group functions are evaluated. Transverse free waves are found to convey no energy. The coupling constant of the axial-vector abelian gauge interaction exhibits asymptotically free ultraviolet behavior, while the self-couplings of the tensor fields do not asymptotically diminish.

Gauge theory of antisymmetric tensor fields

The compact lattice gauge theory of the second-rank antisymmetric tensor field in four dimensions is studied. We calculate the hypersurface tension by Monte Carlo simulation on a 10 4 lattice. It is found that the tension does not go to zero for a finite value of the coupling constant. This suggests that the theory has the confinement phase only. This result is consistent with the result obtained from the dilute gas approximation of the instanton. Some phenomenological implications on the string model are discussed also.

Scale problem in wormhole physics.

Wormhole physics from the quantum thoery of gravity coupled to the second-rank antisymmetric tensor or Goldstone-boson fields leads to an effective potential for these fields. The cosmological energy-density bound is shown to put an upper bound on the cosmological constant which wormhole physics can make zero. This upper bound, of order ${10}^{11}$ GeV, is far smaller than the Planck scale and barely compatible with the possible cosmological constant arising from grand unified theories. In addition, the effect of wormholes on the axion for the strong CP problem is discussed.

Gauge superfield in six dimensions.

In D=6 dimensions the gauge superfield V has a higher gauge freedom than in D=4. In the Wess-Zumino gauge there are no terms with fewer than two Grassmann variables of each type. We find all its tensor components and compute also the chiral superfield strength which contains the linearized curvature tensor of a ``graviton'' field, as well as the field intensities of a ``gravitino,'' a ``photon,'' a ``photino,'' and a trivector whose field strength is a second-rank antisymmetric tensor. The gauge-invariant interaction with a chiral field is given and expressed as a function of the components.