Antisymmetric Tensor Gauge Field Research Articles

Equation of motion forN= 4 supergravity with antisymmetric tensor from its geometric description in central charge superspace

We consider the geometrical formulation in central charge superspace of the N=4 supergravity containing an antisymmetric tensor gauge field. The theory is on-shell, so clearly, the constraints used for the identification of the multiplet together with the superspace Bianchi identities imply equations of motion for the component fields. We deduce these equations of motion in terms of supercovariant quantities and then, we give them in terms of component fields. These equations of motion, deduced from the geometry, without supposing the existence of a Lagrangian, are found to be the same as those derived from the Lagrangian given in the component formulation of this N=4 supergravity multiplet by Nicolai and Townsend.

Remarks on Topological Models and Fractional Statistics

One of the most intriguing aspects of Chern-Simons-type topological models is the fractional statistics of point particles which has been shown essential for our understanding of the fractional quantum Hall effects. Furthermore these ideas are applied to the study of high Tc superconductivity. We present here an recently proposed model for fractional spin with the Pauli term. On the other hand, in D=4 space-time, a Schwarz-type topological gauge theory with antisymmetric tensor gauge field, namely BF model, is reviewed. Antisymmetric tensor fields are conjectured as mediator of string interaction. A dimensional reduction of the previous model provides a (2+1) dimensional topological theory, which involves a 2-form B and a 0-form $\phi$. Some recent results on this model are reported. Recently, there have been thoughts of generalizing unusual statistics to extended objects in others space-time dimensions, and in particular to the case of strings in four dimensions. In this context, discussions about fractional spin and antisymmetric tensor field are presented.

QUANTUM GLOBAL STRINGS AND THEIR CORRELATION FUNCTIONS

A full quantum description of global vortex strings is presented in the framework of a pure Higgs system with a broken global U(1) symmetry in 3+1D. An explicit expression for the string creation operator is obtained, both in terms of the Higgs field and in the dual formulation where a Kalb–Ramond antisymmetric tensor gauge field is employed as the basic field. The quantum string correlation function is evaluated and from this, the string energy density is obtained. Potential application in cosmology (cosmic strings) and condensed matter (vortices in superfluids) are discussed.

'Blowing up' D-branes on non-supersymmetric cycles

In the orbifold limit of K3, one can give exact conformal field theory description of D-branes wrapped on certain non-supersymmetric cycles of K3. We study the effect of switching on the `non-geometric blow up modes' corresponding to anti-symmetric tensor gauge field flux through the 2-cycles on these D-branes. Working to first order in the blow up parameter, we determine the region of the moduli space in which these D-branes are stable. Across the boundary of this region, the D-brane wrapped on the non-supersymmetric cycle decays to a pair of D-branes, each wrapped on a supersymmetric cycle, via a second order phase transition.

THE N=2 VECTOR–TENSOR MULTIPLET, CENTRAL CHARGE SUPERSPACE, AND CHERN–SIMONS COUPLINGS

We present a new, alternative interpretation of the vector–tensor multiplet as a two-form in central charge superspace. This approach provides a geometric description of the (nontrivial) central charge transformations ab initio and is naturally generalized to include couplings of Chern–Simons forms to the antisymmetric tensor gauge field, giving rise to a N=2 supersymmetric version of the Green–Schwarz anomaly cancellation mechanism.

S duality and dyonic p-brane solutions in type II string theory.

We show how a solitonic ``magnetically'' charged p-brane solution of a given supergravity theory, with the magnetic charge carried by an antisymmetric tensor gauge field, can be generalized to a dyonic solution. We discuss the cases of ten-dimensional and eleven-dimensional supergravity in more detail and a new dyonic five-brane solution in ten dimensions is given. Unlike the purely electrically or magnetically charged five-brane solution the dyonic five-brane contains nonzero Ramond-Ramond fields and is, therefore, an intrinsically type II solution. The solution preserves half of the type II spacetime supersymmetries. It is obtained by applying a solution-generating SL(2,R)\ifmmode\times\else\texttimes\fi{}SL(2,R) S duality transformation to the purely magnetically charged five-brane solution. One of the SL(2,R) duality transformations is basically an extension to the type II case of the six-dimensional ${\mathit{Z}}_{2}$ string-string duality. We also present an action underlying the type IIB supergravity theory. \textcopyright{} 1996 The American Physical Society.

SYMPLECTIC QUANTIZATION OF A REDUCIBLE THEORY

We use the symplectic formalism to quantize the Abelian antisymmetric tensor gauge field. It is related to a reducible theory in the sense that all of its constraints are not independent. A procedure like ghost-of-ghost of the BFV method has to be used, but in terms of Lagrange multipliers.

TOPOLOGICAL YANG-MILLS THEORY WITH VECTOR AND ANTISYMMETRIC TENSOR FIELDS

We study a system composed of vector and second rank antisymmetric tensor gauge fields in the superconnection framework. We incorporate the matrix derivative of non-commutative geometry in order to induce the topological Yang-Mills theory. In this structure we get the BRST and anti-BRST transformation rules from one horizontality condition, and obtain the topological classical action naturally from the extended field strength. We obtain its quantum action through the BRST formalism.

ARE THERE TOPOLOGICALLY CHARGED STATES ASSOCIATED WITH QUANTUM ELECTRODYNAMICS?

We present a generalization of quantum electrodynamics (QED) in terms of an antisymmetric tensor gauge field. In this formulation the topological current of this field appears as a source for the electromagnetic field and the topological charge therefore acts physically as an electric charge. The charged states of QED lie in the sector where the topological charge is identical to the matter charge. The antisymmetric field theory, however, admits new sectors where the topological charge is more general. These nontrivial, electrically charged sectors contain massless states orthogonal to the vacuum which are created by a gauge-invariant operator and can be interpreted as coherent states of photons. We evaluate the correlation functions of these states in the absence of matter. The new states have a positive definite norm and do interact with the charged states of QED in the usual way. It is argued that if these new sectors are in fact realized in nature, then a very intense background electromagnetic field is necessary for their experimental observation. The order of magnitude of the intensity threshold is estimated. The value of the quantum of charge is also obtained.

Each Other's Complementary Massless Theory for Totally Antisymmetric Tensor Gauge Fields

Each Other's Complementary Massless Theory for Totally Antisymmetric Tensor Gauge Fields

Each Other's Complementary Massless Theory for Totally Antisymmetric Tensor Gauge Fields

Each other's complementary massless theory for totally antisymmetric tensor gauge fields is given in terms of differential forms. There exist two sequential gauge transformations by which the Faddeev-Popov ghosts are induced sequentially in a covariant quantization using the Becchi-Rouet-Stora transformations

Supergravity and matter: linear multiplet couplings and Kähler anomaly cancellation

We present in detail the properties of a linear multiplet in interaction with supergravity and matter, with a special emphasis on the coupling of Chern-Simons forms, relevant for the problem of the chiral and conformal anomalies in relation with Kähler transformations and the corresponding anomaly cancellations. The linear supermultiplet describes an antisymmetric tensor gauge field together with a dilaton and a Majorana spinor. In particular, these fields are found among the massless modes of superstring theories. We review the general properties of this supermultiplet in the Kähler superspace formalism and construct the complete supersymmetric action. This includes the classically Kähler invariant component field action for all the kinetic terms as well as a Green-Schwarz type action which exhibits a non-holomorphic gauge coupling function.

The R2-action in d=10 conformal supergravity

We present the invariant action for conformal supergravity in ten dimensions. We compare our result to d=6, N=2 conformal supergravity, and show that in d=6 a superconformal invariant based on the Gauss-Bonnet combination must exist. The contributions of the antisymmetric tensor gauge field in d=10 cannot be completely expressed in terms of torsion.

Topological matter coupled to gravity in 2 + 1 dimensions

2 + 1 gravity coupled to a scalar and antisymmetric tensor gauge field is examined. The quantum theory is finite-dimensional and exactly solvable, containing two phase space degrees of freedom in addition to those in the vacuum theory.

The gauged BRST symmetry

We develop a systematic method for constructing the gauged BRST symmetry for any theory. In this framework, the gauged BRST symmetry results as the combination of two basic symmetries of the gauge-fixed theory which one considers: the BRST symmetry and the ghost number symmetry, this latter being promoted to a local one. From this, we can derive a general relation between the BRST and the ghost number Noether currents. We then take advantage of the present method to elaborate on a geometrical algorithm leading to the obtainment of the gauged BRST symmetry for a large class of theories, in arbitrary dimensions of space. These involve systems of antisymmetric tensor gauge fields of arbitrary rank, eventually coupled to gravity. This algorithm allows us to derive algebraically the expressions for the possible consistent anomalies of the BRST Noether current algebras; various examples are explicitly discussed. The gauged BRST symmetry for the free bosonic string is also constructed and used to exhibit the link between the trace anomaly and the nilpotency anomaly of the BRST charge operator. In particular, when the Beltrami parametrization is introduced, we show that the corresponding BRST symmetry can be gauged in a way compatible with the holomorphic factorization. A further use of Ward-Slavnov identities constraining the BRST and ghost number current algebra allows us to recover the well-known local counterterm necessary, at the one-loop level, for rendering the BRST current a good conformal operator.

SPINNING VORTICES IN TYPE II SUPERCONDUCTORS

A field-theoretical model displaying macroscopic type II superconductivity involves electromagnetic and antisymmetric tensor gauge fields interacting in a special background. Vortex lines are represented by Kalb-Ramond strings, and the force law for a vortex in a supercurrent follows naturally. It is shown by a duality transformation that this theory is equivalent to the low-energy sector of a spontaneously broken abelian Higgs model, but the existence of a charged background changes the nature of the symmetry breaking. As a result, it is not Neilsen-Olesen solutions but rather the spinning vortices which describe the macroscopic properties of flux tubes in a superconductor. The relationship with Ginzburg-Landau theory is briefly discussed.

Anti-symmetric tensor gauge theories

Anti-symmetric tensor gauge theories are quantized via the Faddeev-Popov procedure leading to a BRS invariant theory without the need for second order ghosts. The quantum mechanical equivalence of these theories to non-linear sigma models is established using the spontaneously broken global symmetry currents. Upon gauging these symmetries the Higgs mechanism is displayed, while for anomalous symmetries an analog of the Wess-Zumino action is constructed in terms of the anti-symmetric tensor gauge fields.

Lagrangian and Hamiltonian BRST structures of the antisymmetric tensor gauge theory.

We study the Becchi-Rouet-Stora-Tyutin (BRST) structure of a self-interacting antisymmetric tensor gauge field, which has an on-shell null-vector gauge transformation. The Batalin-Vilkovisky covariant general formalism is briefly reviewed, and the issue of on-shell nilpotency of the BRST transformation is elucidated. We establish the connection between the covariant and the canonical BRST formalisms for our particular theory. Finally, we point out the similarities and differences with Witten's string field theory.

Chiral anomaly of antisymmetric tensor fields.

For antisymmetric tensor gauge fields of rank 2n-1 coupled to gravity in 4n dimensions it is shown that the symmetry under duality rotations is broken by quantum effects. The anomaly is related to a local version of the signature index theorem. The \ensuremath{\zeta}-function technique, Fujikawa's method, and the stochastic regularization scheme are discussed.

Gravitational anomalies: Antisymmetric tensor gauge field versus bispinor field

It is shown perturbatively that the gravitational anomaly of the chiral bispinor field is twice as large as that of the self-dual antisymmetric tensor gauge field; in the previous literature they were supposed to agree with each other. This implies that a naive application of Fujikawa's path integral method leads to a wrong result for the anomaly of the self-dual antisymmetric tensor gauge field.