[en] We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial $T^4$ fibrations over Calabi–Yau two-folds. These give rise to eight-dimensional non-Kähler Hermitian manifolds with $SU(4)$ structure. The eight-manifold is also a circle fibration over a seven-dimensional $G_2$ manifold with skew torsion. The eight-manifolds of this type appear as internal manifolds with $SU(4)$ structure in type IIB string theory with $F_3$ and $F_7$ fluxes. These manifolds have generalized calibrated cycles in the presence of fluxes.

[en] We consider the SU(4)-instanton equation on complex-oriented manifolds, introduce the notion of a semiholomorphic structure on bundles over these manifolds, and derive a condition for the notions of holomorphy and semiholomorphy to coincide

[en] A series of lectures is given on the theoretical excitement surrounding the idea of a fourth charmed quark and to provide the foundation necessary to comprehend the rapidly growing literature on this subject. (JFP)

[en] An extension of the interacting boson model (IBM) is suggested by introducing both the particle-hole character and the charge character of the bosons as supplementary degrees of freedom. This allows us to consider an SU(4) symmetry. Within this new classification scheme, three applications are worked out. (author)

No abstract available

[en] A method for finding the reduction of the direct products of two irreducible representations of SU(4) is formulated by tensor method. This formula is applied to some particular cases. (author)

[en] A composite model with hypercolor group being semi-simple gauge group is discussed. A SU(4) x SU(4) composite model with confining weak interactions is proposed, which gives three families of light fermions

[en] We study toric singularities of the form of C⁴/Ga for finite abelian groups Ga/subset SU(4). In particular, we consider the simplest case Ga=/Z₂x/Z₂x/Z₂ and find explicitly charge matrices for partial resolutions of this orbifold by extending the method by Morrison and Plesser. We obtain three kinds of algebraic equations, z₁ z₂ z₃ z₄=z₅², z₁ z₂ z₃=z₄² z₅ and z₁ z₂ z₅ = z₃ z₄ where z_i's parametrize C⁵. When we put N D1 branes at this singularity, it is known that the field theory on the worldvolume of N D1 branes is T-dual to 2x2x2 brane cub model. We analyze geometric interpretation for field theory parameters and moduli space. (author)

[en] The quark-line rule of Okubo-Zweig-Iizuka is generalized to SU(4) by making use of 16-plet mixing angles introduced by the present author. The result is applied to π^-p →eta sub(c)n and π^-p →eta'n relative production rate and some of two-body photonic decays of vector mesons. The experimental results seem to be consistent with the formulation performed in this paper

[en] A quark model in SU(4) is shown and hadrons are classified, weight diagrams are drawn and mathematical aspects of SU(4) symmetry in the light of charmed quantum number are given. (author)