Rank Antisymmetric Tensor Field Research Articles

A SUPERSPACE FORMULATION OF ABELIAN ANTISYMMETRIC TENSOR GAUGE THEORY

We apply a superspace formulation to the four-dimensional gauge theory of a massless Abelian antisymmetric tensor field of rank 2. The theory is formulated in a six-dimensional superspace using rank-2 tensor, vector and scalar superfields and their associated supersources. It is shown that BRS transformation rules of fields are realized as Euler–Lagrange equations without assuming the so-called horizontality condition in an ad hoc manner and that a generating functional [Formula: see text] constructed in the superspace reduces to that of the ordinary gauge theory of Abelian rank-2 antisymmetric tensor field. The WT identity for this theory is derived by making use of the superspace formulation and is expressed in a neat and compact form [Formula: see text].

P-BRANES, POISSON-SIGMA MODELS AND EMBEDDING APPROACH TO (p+1)-DIMENSIONAL GRAVITY

A generalization of the embedding approach for d-dimensional gravity based upon p-brane theories is proposed. We prove that the D-dimensional p-brane coupled to an antisymmetric tensor field of rank (p+1) provides the dynamical basis for the description of d=(p+1)-dimensional gravity in the isometric embedding formalism. By that we mean that the equations of motion following from this action describe any (p+1)-dimensional space–time (at least locally) once the antisymmetric tensor field is chosen appropriately. "Physical" matter appears in such an approach as a manifestation of a D-dimensional antisymmetric tensor (generalized Kalb–Ramond) background. For the simplest case, the Lorentz harmonic formulation of the bosonic string in a Kalb–Ramond background and its relation to a first order Einstein–Cartan approach for (d=2)-dimensional gravity is analyzed in some detail. We show that a general Poisson-sigma model structure emerges in this case. For the minimal choice of a free D=3 string an interesting "dual" formulation is found which has the structure of a Jackiw–Teitelboim theory, coupled minimally to a massive scalar field. Our approach is intended to serve as a preparation for the study of d-dimensional supergravity theory, either starting from the generalized action of free supersymmetric (d-1)-branes or D(d-1)-branes, or from the corresponding geometric equations ("rheotropic" conditions).

DUALITY INVARIANCE OF COSMOLOGICAL SOLUTIONS WITH TORSION

We show that for a string moving in a background consisting of maximally symmetric gravity, dilaton field and second rank antisymmetric tensor field, the O(d) ⊗ O(d) transformation on the vacuum solutions gives inequivalent solutions that are not maximally symmetric. We then show that the usual physical meaning of maximal symmetry can be made to remain unaltered even if torsion is present and illustrate this through two toy models by determining the torsion fields, the metric and Killing vectors. Finally we show that under the O(d) ⊗ O(d) transformation this generalized maximal symmetry can be preserved under certain conditions. This is interesting in the context of string related cosmological backgrounds.

DUALITY SYMMETRIES IN NONLINEAR GAUGE THEORIES

Duality symmetries are discussed for nonlinear gauge theories of (n-1)th rank antisymmetric tensor fields in general even dimensions d=2n. When there are M field strengths and no scalar fields, the duality symmetry groups should be compact. We find conditions on the Lagrangian required by compact duality symmetries and show an example of duality invariant nonlinear theories. We also discuss how to enlarge the duality symmetries to noncompact groups by coupling scalar fields described by nonlinear sigma models.

Faddeev-Jackiw analysis of topological mass-generating action

We analyze the gauge symmetry of a topological mass generating action in four dimensions which contains both a vector and a second rank antisymmetric tensor fields. In the Abelian case, this system induces an effective mass for the vector gauge field via a topological coupling $B \wedge F$ in the presence of a kinetic term for the antisymmetric tensor field $B$, while maintaining a gauge symmetry. On the other hand, for the non-Abelian case the $B$ field does not have a gauge symmetry unless an auxiliary vector field is introduced to the system. We analyze this change of symmetry in the Faddeev-Jackiw formalism, and show how the auxiliary vector field enhances the symmetry. At the same time this enhanced gauge symmetry becomes reducible. We also show this phenomenon in this analysis.

Algebraic renormalization of the BF Yang-Mills theory

We discuss the quantum equivalence, to all orders of perturbation theory, between the Yang-Mills theory and its first order formulation through a second rank antisymmetric tensor field. Moreover, the introduction of an additional nonphysical vector field allows us to interpret the Yang-Mills theory as a kind of perturbation of the topological BF model.

String-Like Description of Gravity and Possible Applications for F-Theory

The Lorentz harmonic formulation of D-dimensional bosonic p-brane theory with D≥ (p+1)(p+2)/2 coupled to an antisymmetric tensor field of rank d=(p+1) provides the dynamical ground for the description of d=(p+1) dimensional gravity. Hence it realizes the idea of Regge and Teitelboim on a "string-like" description of gravity. The simplest nontrivial models of such a kind are provided by free D-dimensional p-branes in which world–volumes are embedded as minimal surfaces. Possible applications of such a model with d=2+2 and D=2+10 for studying a geometry of bosonic sector of F-theory are considered. Some speculations inspired by the proposed model are presented.

Extended dualization: A method for the bosonization of anomalous fermion systems in arbitrary dimension.

The technique of extended dualization developed in this paper is used to bosonize quantized fermion systems in arbitrary dimension $D$ in the low energy regime. In its original (minimal) form, dualization is restricted to models wherein it is possible to define a dynamical quantized conserved charge. We generalize the usual dualization prescription to include systems with dynamical nonconserved quantum currents. Bosonization based on this extended dualization requires the introduction of an additional rank 0 (scalar) field together with the usual antisymmetric tensor field of rank ($D\ensuremath{-}2$). Our generalized dualization prescription permits one to clearly distinguish the arbitrariness in the bosonization from the arbitrariness in the quantization of the system. We study the bosonization of four-fermion interactions with a large mass in arbitrary dimension. First, we observe that dualization permits one to formally bosonize these models by invoking the bosonization of the free massive Dirac fermion and adding some extra model-dependent bosonic terms. Second, we explore the potential of extended dualization by considering the particular case of chiral four-fermion interactions. Here minimal dualization is inadequate for calculating the extra bosonic terms. We demonstrate the utility of extended dualization by successfully completing the bosonization of this chiral model. Finally, we consider two examples in two dimensions which illuminate the utility of using extended dualization by showing how quantization ambiguities in a fermionic theory propagate into the bosonized version. An explicit parametrization of the quantization ambiguities of the chiral current in the chiral Schwinger model is obtained. Similarly, for the sine-Gordon interaction in the massive Thirring model the quantization arbitrariness is explicitly exhibited and parametrized.

Duality and bosonisation in arbitrary dimensions

A functional integral approach is developed to discuss the bosonisation of the massive Thirring and the massive Schwinger models in arbitrary D dimensions. It is found that these models, to all orders in the inverse fermi mass, bosonise to a theory involving a usual gauge field and a ( D − 2) rank antisymmetric (Kalb-Ramond) tensor field. Explicit bosonisation identities for the fermion current are deduced. Specializing to the lowest order reveals (for any D ≥ 4) a mapping between the massive Thirring model and the Proca model. It also establishes an exact duality between the Proca model and the massive ( D − 2) rank Kalb-Ramond model. Schwinger terms in the current algebra are computed. Conventional bosonisation results in D = 2, 3 are reproduced.

Topological Yang–Mills theory from non-commutative geometry

It will be shown that the topological Yang–Mills theory of Witten can be induced from the usual Yang–Mills theory of the second rank antisymmetric tensor field when the matrix derivative of non-commutative geometry proposed by Connes is incorporated in the superconnection framework. It is done by identifying consistently the antisymmetric tensor field B with the usual field strength F by B=−F.

ANTISYMMETRIC TENSOR FIELD COUPLED TO CHIRAL MATTER AND DYNAMICAL SYMMETRY BREAKING

The minimal coupling of chiral fermions to a second rank antisymmetric tensor field is considered, and an alternative to the standard model is discussed in which the Higgs doublet is replaced by a real scalar and a second rank antisymmetric tensor. The dynamical breaking of electroweak symmetry, via the Nambu-Jona-Lasinio mechanism, is shown to occur due to natural four-Fermi interactions. The mean field theory due to instanton configurations in the antisymmetric tensor field is also presented and possible cosmological applications of this model are discussed.

Axionic instantons and the creation of expanding universes

Abstract In a class of models of scalar matter coupled to N = 1 supergravity, we investigate the existence of gravitational instantons that correspond to the creation of expanding universes. Expressing the derivatively coupled pseudoscalar field in terms of a second rank antisymmetric tensor field (axion), we show that, under mild assumptions about the scalar potential, the theory possesses axion-induced gravitational instanton solutions with the desired interpretation. The assumptions made can be met in the effective four-dimensional theory obtained in a particular compactification of the zero-slope limit of the ten-dimensional superstring theory. Such a system offers an appealing framework for the natural realization of the recent idea that coupling constants, including the cosmological constant, are determined by universal dynamics.

Conformally covariant equation of second rank antisymmetric tensor field

The manifestly SO(4,2) invariant equation of second rank antisymmetric tensor field is got in 6-dimensional space with subsidiary conditions. These equations lead naturally to conformally covariant field equation that we obtained in Minkowski space.

Conformally Covariant Theory of Second Rank Antisymmetric Tensor Field

The conformally covariant field equation on second rank antisymmetric tensor is derived and its conformally covariant energy-momentum tensor is also obtained.

A quantum cosmological approach to Kaluza-Klein theory and the boundary condition of 'no boundary'

A quantum cosmological model of the Kaluza-Klein theory is investigated. The Wheeler-De Witt equation of (D+1)-dimensional gravity with a (D-4)th rank antisymmetric tensor field (ATF) is analysed, restricted to a minisuperspace of topology R*S3*Sn. The initial condition problem is discussed and the boundary condition of 'no boundary' for a universe corresponding to a manifold with topology of Kaluza-Klein type is formulated. However, in the minisuperspace approximation of Kaluza-Klein theory, the definition of the boundary condition of 'no boundary' becomes obscure and the problem is discussed. The analysis, using the WKB approximation, shows that a subclass of classical paths which contribute to the wavefunction consists of bounce solutions. Furthermore, it is found that initial values of the classical paths, leading to universes of large scale and a compactified internal space of Planck size, can be localised in a very restricted region.

Stability of classical solutions in extended Kaluza-Klein theories

The stability of classical solutions for a scalar field corresponding to the radius of S n = SO( n + 1)/SO( n) in extended Kaluza-Klein theories is investigated. A stable solution is shown to emerge if an antisymmetric tensor field of rank n−1 or rank-three acquires a nonzero background field strength in S n or in four-dimensional spacetime, respectively.

SO(4) gauging of N = 2 supergravity in seven dimensions

We obtain N = 2 supergravity theory coupled to N = 2 matter by truncation of the N = 4 theory in seven dimensions. The truncated theory possess global GL(4, R) ⊗ local composite SO(4) invariance. We then gauge the global SO(4) subgroup of GL(4, R), and preserve the composite SO(4) symmetry, following the method of de Wit and Nicolai in d = 4. The resulting action has a potential which contains all ten scalars of the theory. The single second rank antisymmetric tensor field in the theory has a generalized field strength, which contains the Chern-Simons three-form.

Dynamics of dimensional reduction

In d-dimensional unified theories that, along with gravity, contain an antisymmetric tensor field of rank s-1, preferential compactification of d- s or of s space-like dimensions is found to occur. This is the case in 11-dimensional supergravity where s = 4.