Tensor Field Theory Research Articles

Condensation of topological defects and confinement

We study the static quantum potential for a theory of antisymmetric tensor fields that results from the condensation of topological defects, within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy is the sum of a Yukawa and a linear potentials, leading to the confinement of static probe charges.

On unconstrained SU(2) gluodynamics with theta angle

The Hamiltonian reduction of classical SU(2) Yang-Mills field theory to the equivalent unconstrained theory of gauge invariant local dynamical variables is generalized to the case of nonvanishing theta angle. It is shown that for any theta angle the elimination of the pure gauge degrees of freedom leads to a corresponding unconstrained nonlocal theory of self-interacting second rank symmetric tensor fields, and that the obtained classical unconstrained gluodynamics with different theta angles are canonically equivalent as on the original constrained level.

5D actions for 6D self-dual tensor field theory

We present two equivalent five-dimensional actions for six-dimensional (N,0) N=1,2 supersymmetric theories of self-dual tensor whose one spatial dimension is compactified on a circle. The Kaluza-Klein tower consists of a massless vector and infinite number of massive self-dual tensor multiplets living in five-dimensions. The self-duality follows from the equation of motion. Both actions are quadratic in field variables without any auxiliary field. When lifted back to six-dimensions, one of them gives a supersymmetric extension of the bosonic formulation for the chiral two-form tensor by Perry and Schwarz.

Description of Photon and Notoph Degrees of Freedom by Proca-like Equations

In the sixties Ogievetski and Polubarinov proposed a concept of a notoph, whose helicity properties are complementary to those of a photon. Then, this theory pepetually received the name of Kalb and Ramond. We analyze the theory of antisymmetric tensor fields in the view of the normalization problem. The obtained result is that it is 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. We also briefly discuss recently claimed terms σ · [A × A*].

Stochastic vector and tensor fields applied to strain modelling

In this paper a brief introduction to the theory of stochastic vector and tensor fields is given. Necessary and sufficient conditions for isotropic vector random fields are reviewed and necessary conditions for second order tensors are developed. These models increase the flexibility of the usual geostatistical models but at the cost of increased complexity. This complexity can be reduced to a manageable level for a class of tensor fields that are associated with strain. The potential for modelling fractures using strain models is briefly discussed.

Nonsymmetrical tensor potential in the relativistic theory of gravity

We suggest a theory of nonsymmetrical tensor fields in the Minkowski space. This theory generalizes the relativistic theory of gravity with a symmetrical potential and preserves all its basic postulates. The connection of the effective space-time in which the gravitational field equations can be represented possesses torsion and nonmetricity.

Linking observables in perturbed topological field theories

The topological antisymmetric tensor field theory in n-dimensions is perturbed by the introduction of local metric dependent interaction terms in the curvatures. The correlator describing the linking number between two surfaces in n-dimensions is shown to be not affected by the quantum corrections.

Lagrangian Theory of Tensor Fields over Spaces with Contravariant and Covariant Affine Connections and Metrics and Its Application to Einstein's Theory of Gravitation in V 4 Spaces

The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and a metric \([(\bar L_n ,g) - spaces]\) is considered. The functional, the Lie, the covariant, and the total variations of a Lagrangian density, depending on components of tensor fields (with finite rank) and their first and second covariant derivatives, are established. A variation operator is determined and the corollaries of its commutation relations with the covariant and the Lie differential operators are found. The canonical (common) method of Lagrangians with partial derivatives (MLPD) and the method of Lagrangians with covariant derivatives (MLCD) are outlined. They differ each other by the commutation relations the variation operator has to obey with the covariant and the Lie differential operator. The covariant Euler–Lagrange equations are found on the basis of the MLCD. The energy-momentum tensors are considered on the basis of the Lie variation and the covariant Noether identities.

EINSTEIN'S THEORY OF GRAVITATION AS A LAGRANGIAN THEORY FOR TENSOR FIELDS

Einstein's theory of gravitation (ETG) is considered as a Lagrangian theory of tensor fields over (pseudo) Riemannian spaces without torsion (Vn spaces, n=4) by means of the method of Lagrangians with covariant derivarives (MLCD). In a trivial manner Euler–Lagrange's equations as Einstein's equations are obtained. The corresponding energy–momentum tensors (EMT's) are found for the standard for the ETG Lagrangian invariant on the basis of the covariant Noether identities. The symmetric energy–momentum tensor of Hilbert appears as an element irrelevant to the whole scheme of the considered Lagrangian thoery of tensor fields over Vn spaces despite of the fact that it has some elements of the structure of the variational EMT of Euler–Lagrange. The notion of the active gravitational rest mast density is related to the variational EMT of Euler–Lagrange and on this basis to a certain extent to the EMT of Hilbert.

P-BRANES AS COMPOSITE ANTISYMMETRIC TENSOR FIELD THEORIES

p′-brane solutions to rank p+1 composite antisymmetric tensor field theories of the kind developed by Guendelman, Nissimov and Pacheva are found when the dimensionality of space–time is D=(p+1)+(p′+1). These field theories possess an infinite-dimensional group of global Noether symmetries, that of volume-preserving diffeomorphisms of the target space of the scalar primitive field constituents. Crucial in the construction of p′ brane solutions are the duality transformations of the fields and the local gauge field theory formulation of extended objects given by Aurilia, Spallucci and Smailagic. Field equations are rotated into Bianchi identities after the duality transformation is performed and the Clebsch potentials associated with the Hamilton–Jacobi formulation of the p′ brane can be identified with the duals of the original scalar primitive constituents. Explicit examples are worked out the analog of S and T duality symmetry are discussed. Different types of Kalb–Ramond actions are given and a particular covariant action is presented which bears a direct relation to the light cone gauge p-brane action.

Duality and global symmetries

This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and non-abelian T-duality in string theory, abelian and nonabelian bosonization, and duality for massless and massive antisymmetric tensor field theories in arbitrary number of dimensions. Open questions regarding these techniques are also discussed. (Lectures given at 33rd Karpacz Winter School `Duality: Strings and Fields' .)

Phases of antisymmetric tensor field theories

We study the different phases of field theories of compact antisymmetric tensors of rank h − 1 in arbitrary space-time dimensions D = d + 1. Starting in a ‘Coulomb’ phase, topological defects of dimension d − h − 1 (( d − h − 1)-branes) may condense leading to a generalized ‘confinement’ phase. If the dual theory is also compact the model may also have a third, generalized ‘Higgs’ phase, driven by the condensation of the dual ( h − 2)-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low-energy effective action for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the Coulomb phase but massive for the Higgs and confinement phases. We illustrate our prescription in detail for compact QED in 4D. Compact QED and O(2) models in 3D, as well as a periodic scalar field in 2D (strings on a circle), are also discussed. In this last case we show how T-duality is maintained if one considers both world-sheet instantons and their duals. We also unify various approaches to the problem of the axion mass in 4D string models. Finally we discuss possible implications of our results for non-perturbative issues in string theory.

Condensation of p-Branes and Generalized Higgs/Confinement Duality

We review our recent work on the low-energy actions and the realizations of strong-weak coupling dualities in non-perturbative phases of compact antisymmetric tensor field theories due to p-brane condensation. As examples we derive and discuss the confining string and confining membrane actions obtained from compact vector and tensor theories in 4D. We also mention the relevance of our results for the description of the Hagedorn phase transition of finite temperature strings.

Massless Limits of Massive Tensor Fields. II: Infrared Regularizaiton of the Fierz-Pauli Model

Izawa's gauge-fixing procedure based on BRS symmetry is applied twice to the massive tensor field theory of Fierz-Pauli type. It is shown the second application can remove massless singularities which remain after the first application. Massless limit of the theory is discussed.

Non-Abelian gauge antisymmetric tensor fields

We construct the theory of non-abelian gauge antisymmetric tensor fields, which generalize the standard Yang-MIlls fields and abelian gauge p-forms. The corresponding gauge group acts on the space of inhomogeneous differential forms and it is shown to be a supergroup. The wide class of generalized Chern-Simons actions is constructed.

The Complementary Scheme for Massive Totally Antisymmetric Tensor Field Theories

The Complementary Scheme for Massive Totally Antisymmetric Tensor Field Theories

The Complementary Scheme for Massive Totally Antisymmetric Tensor Field Theories

We demonstrate the complementary scheme for massive totally antisymmetric tensor field theories. The differential geometry plays a crucial role in this formulation

Is the Stochastic Gauge-Fixing a Consistent Method for Reducible Gauge Theories?

By using the Stochastic Gauge-Fixing term derived in a previous paper, we stochastically quantize the Non-Abelian Antisymmetric Tensor Field theory as an example of the Reducible Gauge Theories. Though all the quantities are finitely computed and the induced vertex really reproduces the full ghost contributions, the uninterpretable terms still remain.

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.

A supersymmetric theory of even-rank antisymmetric tensor fields

We present a theory of rank-2 k antisymmetric tensor fields (or equivalently, of differential 2 k-forms) on a world-surface of dimension 4 k + 1. In addition gauge symmetries, the theory exhibits an unconventional supersymmetry. We examine the unusual interplay between these two types of symmetries in the process of gauge fixing. We interpret the gauge-fixed supercharge as a Dirac operator on an appropriate coset space of differential forms: in particular, the k = 1 theory yields the Dirac operator on the space of two-forms modulo exact two-forms on a manifold of dimension 4.