Modern Physics Letters A

We discuss a quantum-theoretical aspect of the massive Abelian antisymmetric tensor gauge theory with antisymmetric tensor current. To this end, an Abelian rank-2 antisymmetric tensor field is quantized both in the covariant gauge with an arbitrary gauge parameter and in the axial gauge of the Landau type. The covariant quantization yields the generating functional written in terms of an antisymmetric tensor current and its divergence. Origins of the terms in the generating functional are clearly understood in comparison with the quantization in the unitary gauge. The quantization in the axial gauge with a suitable axis directly yields the generating functional which is the same as that obtained by using Zwanziger's formulation for electric and magnetic charges. It is shown that the generating functionals lead to a composite of the Yukawa and the linear potentials.

Explicit solutions to the conifold equations with complex dimension n = 3, 4 in terms of complex coordinates (fields) are employed to construct the Ricci-flat Kähler metrics on these manifolds. The Kähler two-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of two-dimensional nonlinear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the "integration constants", arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be non-singular. As the target space is Ricci-flat, the perturbative one-loop counterterms being absent, the model becomes topological. The inherent U(1) fiber over the base of the conifolds is shown to correspond to a gauge connection in the sigma model.

The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action for a nonlinear sigma model with resolved conifold as target space, is found to have a minimum value, which is topological. The metric is expressed in terms of the six real coordinates and compared with earlier works. The harmonic function, which is the warp factor in Type II-B string theory, is obtained and the ten-dimensional warped metric has the AdS₅ × X₅ geometry.

Instead of anchoring the seesaw mechanism with the conventional heavy right-handed neutrino singlet, a small Majorana neutrino mass may be obtained just as well with the addition of a heavy triplet of leptons per family to the minimal standard model of particle interactions. The resulting model is shown to have the remarkable property of accommodating a new U(1) symmetry which is anomaly-free and may thus be gauged. There are many possible phenomenological consequences of this proposal which may already be relevant in explaining one or two recent potential experimental discrepancies.

In this work we develop a new version of the fuzzy bag model. The new feature is the inclusion of energy–momentum conservation. This turns the model into a "real" bag model, as opposed to a relativistic potential model. One immediate consequence is that the bag constant B will acquire a radial dependence, B = B(r), whose functional form can be completely fixed without any arbitrariness. Such a feature is of importance in the study of neutron stars, where a radial dependence of B is usually put in by hand. The parameters of the model are found by fitting the masses of the baryon octet. We include center-of-mass, one-gluon exchange and pion exchange corrections for these masses.

The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In particular, the traditional approach of quantizing a space–time metric is criticized and two possible avenues for constructing a satisfactory theory are put forward.