Modern Physics Letters A

We introduce a simple dynamical scheme to supplement the complementarity and Higgs phase analyses of composite models with semi-simple metacolor groups. The critical couplings which signal the dynamical breakdown of the various simple groups contained in the metacolor semi-simple group determine the order of appearance of the condensates of the simple groups. Together with the Higgs phase analysis, it helps to determine the global symmetry of the fermion composite. The global symmetry group will eventually be gauged to form the low energy dynamical symmetry group of the composite.

In place of Dirac monopoles with string, we have recently introduced “monopoles without string” on the basis of a generalized potential, the sum of a vector A and a pseudovector γ₅B potential. By having recourse to the (graded) Clifford algebra which allows adding together tensors of different ranks (e.g., scalars+pseudoscalars+vectors+pseudovectors+...), in a previous paper we succeeded in constructing a lagrangian and hamiltonian formalism for interacting monopoles that can be regarded as satisfactory from various points of view. In the present note, after having completed that formalism, we put forth a purely geometrical interpretation of it within the Kähler algebra on differential forms, essential ingredients being the natural introduction of a “generalized curvature” and the Hodge decomposition. We thus pave the way for the extension of our “monopoles without string” to non-abelian gauge groups. The analogies of this approach with supersymmetric theories are apparent.

A one-loop tadpole and a one-loop two-string counterterms are proposed, capable of restoring BRST invariance to the respective scattering amplitudes of polyhedral closed string field theory.

We define a superconformal algebra with the central charge c=3d, which is the symmetry of the non-linear σ model on a complex d dimensional Calabi-Yau manifold. The c=3d algebra is an extended superconformal algebra obtained by adding the spectral flow generators to the N=2 superconformal algebra. We study the representation theory and show that its representations are invariant under the integer-shift spectral flow. We present the character formulas and their modular transformation properties. We also discuss the relation to the N=4 superconformal algebra.

Classical vortex solutions in a three-dimensional supersymmetric Abelian-Higgs model are presented. A cylindrically symmetric ansatz for the bosonic and fermionic fields is used, and the asymptotic behavior for these fields are also obtained. No electric charge for this model is found, although the temporal component for the bosonic gauge field is not zero. Finally, after we have integrated over all the fermionic degree of freedom, a purely bosonic action is obtained.

We show, using path integral methods, that a complex scalar field in 2+1 dimensions coupled to an abelian gauge field with Chern-Simons action is equivalent to a free Dirac fermion. We show the equivalence of the vacuum functional and construct the fermion fields explicitly. Our proof is independent of the long wavelength approximation.

The deviations from standard model predictions for the pair production of Z⁰ at e⁺e⁻ colliders with the inclusion of mixing between ordinary and exotic leptons are evaluated for (i) the differential cross section and (ii) the longitudinal polarization asymmetry at LEP II and at possible the next linear collider energies. For heavy exotic leptons (m_E ~ 250 GeV) the deviations have distinctive features that could allow the possibility of distinguishing between mirror, vector-doublet and vector-singlet type of exotic lepton mixings.

The Higgs mechanism is investigated for the affine version of the N=4 Yang-Mills theory.