Kalb-Ramond Gauge Field Research Articles

Aspects of a noncommutative scalar/tensor duality

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical $U(1)$ gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in $\ensuremath{\theta}$. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The $p$-form generalization of the Seiberg-Witten map to order $\ensuremath{\theta}$ is also derived.

The fundamental non-critical string

We obtain the (super) gravity solution in arbitrary space–time dimension less than ten, that gives a low energy description of a fundamental string embedded in a non-critical vacuum, product of d -dimensional Minkowski space–time and a cigar-like geometry with scale r 0 . This solution, one of the few known examples of objects doubly localized, both at the origin of the transverse space as well as at the tip of the cigar, is determined by its charge Q under the Kalb–Ramond gauge field B , and presumably preserves, for even d , 2 d 2 supercharges. Moreover, we show that the solution is reliable at least in a region far away from both origins, as it is the case with the well known branes of critical string theory.

Gauge theories of Josephson junction arrays

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with a periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system with an antisymmetric Kalb-Ramond gauge field.

Gauge theory of relativistic membranes

A relativistic membrane is usually represented by the Dirac-Nambu-Goto action in terms of the extremal area of a three-dimensional timelike submanifold of Minkowski space. The authors show that a relativistic membrane admits an equivalent representation in terms of the Kalb-Ramond gauge field Fmu nu rho = delta ( mu Bnu rho ) encountered in string theory. At first glance this is somewhat surprising, since the Kalb-Ramond field is usually interpreted as the spin-0 radiation field generated by a closed string. By 'equivalence' of the two representations they mean the following. If x=X( xi ) is a solution of the classical equations of motion derived from the Dirac-Nambu-Goto action, then it is always possible to find a differential form of rank 3, satisfying Maxwell-type equations, such that, in a coordinate basis: Fmu nu rho (X( xi ))=constant*Xmu nu rho N-(1/3!)Xalpha beta gamma Xalpha beta gamma where Xmu nu rho represents the tangent 3-vector to the membrane world-track. The converse proposition is also true. They show that a relativistic membrane, regarded as a mechanical system, admits a Hamilton-Jacobi formulation in which the H-J function describing a family of classical membrane histories is given by F=dB=dS1 V-product dS2 V-product dS3 where the three scalar functions Si(x) are the Clebsch potentials. They introduce a new Lagrangian of the Kalb-Ramond type which provides a first-order formulation for both open and closed membranes. The advantage of the Lagrangian approach is that it shows explicitly the correspondence between the gauge formulation of the membrane in terms of the Kalb-Ramond potential and the geometric formulation of the membrane in terms of the mechanical coordinates Xmu ( xi ). Finally, for completeness, they show that such a correspondence can be established in the very general case of a p-brane coupled to gravity in a spacetime of arbitrary dimensionality.

Higgs mechanism for Kalb-Ramond gauge field.

Kalb-Ramond gauge field theory, coupled to manifestly gauge-invariant and reparametrization-invariant second-quantized string fields, is studied. String condensation into the vacuum is shown to develop masses to the Kalb-Ramond gauge field which we call the string Higgs mechanism. In case the Kalb-Ramond field couples to the open strings which have a massless vector field in the spectrum, our field theory also exhibits the well-known Stueckelberg mechanism. To strengthen our conclusion, we construct a lattice version of the above string field theory and demonstrate that the mean-field approximation indicates the existence of the Higgs phase.