Modern Physics Letters A

We consider a class of Calabi-Yau compactifications which are constructed as a complete intersection in weighted projective space. For manifolds with one Kähler modulus we construct the mirror manifolds and calculate the instanton sum.

We generalize the quantum group structure of two-dimensional nonrelativistic electron in a uniform magnetic field into the case of a many-particle system on a torus. We verify the conjecture that the deformation parameter of the quantum algebra is given by the filling factor ν=1/p (p odd) on the basis of the Haldane-Rezayi’s wave functions.

We study the neutrino masses and mixings in the flipped SU(5) model assuming the Dimopoulos-Hall-Raby type mass matrices. The neutrino masses are evolved down to low energies by using the renormalization group equation of the effective seesaw mass operator. The ν_τ mass and the ν_µ−ν_τ mixing are predicted by using the solar neutrino data. The predicted mass is consistent with the condition of the hot dark matter expected from COBE results. Our results are also compared with the ones in SO(10). Although the large ν_µ−ν_τ mixing could be obtained in our model, the ν_τ mass is too small to be consistent with the atmospheric muon neutrino deficit from KAMIOKA and IMB.

The dynamical question is raised of the possible existence of long-range, residual attractive forces between hadrons due to the overall color-neutral exchange of two, massless transverse gluons between their constituents. Such a force between fermionic constituents would behave as 1/R6. We discuss the experiments which measure the real part of the nuclear amplitude, through its interference with the Coulomb amplitude in high energy elastic scattering at very small momentum transfers. We show that on-going experiments at and at 1800 GeV are sensitive to the scattering amplitude from a residual long-range force.

We demonstrate a simple contradiction of naive deterministic theories with quantum mechanics by showing that the spin components cannot have deterministic values for many values of the total spin of a particle. Using a theorem in number theory, we work out the complete set of spin values which display such properties. The fact that the set is infinite should prompt some modifications in the usual statement about achieving the classical limit when the value of angular momentum becomes very large.

Using the BFV approach we quantize a pseudoclassical model of the spin-1/2 relativistic particle that contains a single bosonic constraint, contrary to the usual locally supersymmetric models that display first and second class constraints.

The recent measurements of R_b=Γ_b/Γ_had together with other experimentally independent measurements of weak neutral current observables at LEP/SLC, display excellent internal self-consistency if the top dependent vertex correction is ignored. Extending this consistency further, the possibility of ignoring even the propagator/oblique corrections is not ruled out. Being a clean top mass indicator within SM, free from Higgs and strong interaction uncertainty, a comparison of R_b with the directly measured top quark mass at Tevatron clearly strengthens the above view. To preserve the weak radiative corrections of SM origin, for which evidence exists from measurements at low energies, independent of LEP/SLC, the most natural choice would be to invoke new radiative corrections of opposite sign from physics beyond SM. We stress that an improved measurement of R_b at LEP/SLC together with the direct measurement of top quark mass at Tevatron will play a clean and decisive role in this direction.

It is argued that singular vectors of the topological conformal (twisted N=2) algebra are identical with singular vectors of the sl(2) Kac-Moody algebra. The derivation uses the (twisted) Kazama-Suzuki model associated with sl(2)/u(1). This Kazama-Suzuki construction can also be combined with the realization of topological symmetry in matter+gravity theories to produce a representation for the sl(2) current algebra in terms of an arbitrary minimal matter dressed with additional fields. The Malikov-Feigin-Fuchs (MFF) formula for sl(2) singular vectors translates into a general expression for topological singular vectors in matter+gravity theories. The MFF/topological singular states are observed to vanish in Witten’s free-field construction of the (twisted) N=2 algebra, derived from the Landau-Ginzburg formalism.