International Journal of Modern Physics A

The fermion generation puzzle has survived into this century as one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a non-Abelian generalization of electric–magnetic duality. First, by constructing in loop space a non-Abelian generalization of the Abelian dual transform (Hodge *), one finds that a "magnetic" symmetry exists also in classical Yang–Mills theory dual to the original ("electric") gauge symmetry. Secondly, from a result of 't Hooft's, one obtains that for confined color SU(3), the dual symmetry is spontaneously broken and can play the role of the "horizontal symmetry" for generations. Thirdly, such an identification not only offers an explanation why there should be three and apparently only three generations of fermions with the remarkable mass and mixing patterns seen in experiment, but allows even a calculation of the relevant parameters giving very sensible results. Other testible predictions follow ranging from rare hadron decays to cosmic ray air showers.

A model independent search for Abelian Z′ gauge boson in four-fermion processes is analyzed. It is based on a low energy effective Lagrangian parametrizing the Z′ interactions with the fermion and scalar fields of the Standard Model. These parameters are related due to the requirement of renormalizability (gauge invariance). It is found that the absolute value of the Z′ coupling to the axial-vector currents is the same for all fermions and it is strongly correlated with the Z′ coupling to the scalar field. On the base of these relations the dependences between the parameters of the effective Lagrangian constructed from dimension-six operators are derived.

Considering a class of (2, 0)-super-Yang–Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here their coupling to ordinary matter and to nonlinear σ-models in (2, 0)-superspace. The dynamics and the couplings of the gauge potentials are discussed and the interesting feature that comes out is a sort of "chirality" for one of the gauge potentials once light-cone coordinates are chosen.

Using the analogy of a well-known mathematical formalism, an analytical form of the probability density of a hadron as a quarkonium system has been suggested which corresponds to that obtained from the statistical model. The aforesaid prescription also offers the necessary framework to incorporate different orders of approximations in it. Unlike all existing theoretical approaches, the model reveals the fractal characteristics of a hadron, like the fractal dimension D_F, correlation dimension D_C and the anomalous dimension D_A. The direct physical bearings of these dimensional quantities on the physical parameters related to the recent experimental data have also been discussed.

We formulate an effective Schrödinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization group equation to the world sheet partition function of a deformed σ-model describing the system, which includes the quantum recoil due to the exchange of string states between the individual D-particles. We arrive at an effective Fokker–Planck equation for the probability density with diffusion coefficient determined by the total kinetic energy of the recoiling system. We use Galilean invariance of the system to show that there are three possible solutions of the associated nonlinear Schrödinger equation depending on the strength of the open string interactions among the D-particles. When the open string energies are small compared to the total kinetic energy of the system, the solutions are governed by freely-propagating solitary waves. When the string coupling constant reaches a dynamically determined critical value, the system is described by minimal uncertainty wavepackets which describe the smearing of the D-particle coordinates due to the distortion of the surrounding space–time from the string interactions. For strong string interactions, bound state solutions exist with effective mass determined by an energy-dependent shift of the static BPS mass of the D0-branes.

We discuss the properties of matter in a D-dimensional anti-de Sitter-type space–time induced dynamically by the recoil of a very heavy D(irichlet)-particle defect embedded in it. The particular form of the recoil geometry, which from a world sheet view point follows from logarithmic conformal field theory deformations of the pertinent sigma-models, results in the presence of both infrared and ultraviolet (spatial) cutoffs. These are crucial in ensuring the presence of mass gaps in scalar matter propagating in the D-particle recoil space–time. The analogy of this problem with the Liouville-string approach to QCD, suggested earlier by John Ellis and one of the present authors, prompts us to identify the resulting scalar masses with those obtained in the supergravity approach based on the Maldacena's conjecture, but without the imposition of any supersymmetry in our case. Within reasonable numerical uncertainties, we observe that agreement is obtained between the two approaches for a particular value of the ratio of the two cutoffs of the recoil geometry. Notably, our approach does not suffer from the ambiguities of the supergravity approach as regards the validity of the comparison of the glueball masses computed there with those obtained in the continuum limit of lattice gauge theories.

The κ-invariant and supersymmetric actions of D1 and D5-branes in AdS₃×S³ are investigated, as well as the action of a D5-brane in an AdS₅×S⁵ background. The action of a D5-brane lying totally in an AdS₃×S³ background is found. Some progress was made towards finding the action for the D5-brane free to move in the whole AdS₃×S³×T⁴ space, however the supersymmetric action found here is not κ-invariant and the reasons the method used did not find a κ-invariant solution are discussed.

Inclusive bottom hadron decays are analyzed based on the heavy quark effective field theory (HQEFT). Special attentions in this paper are paid to the b→u transitions and nonspectator effects. As a consequence, the CKM quark mixing matrix elements |V_ub| and |V_cb| are reliably extracted from the inclusive semileptonic decays B→X_ueν and B→X_ceν. Various observables, such as the semileptonic branch ratio B_SL, the lifetime differences among B^-, B⁰, B_s and Λ_b hadrons, the charm counting n_c, are predicted and found to be consistent with the present experimental data.

It is known for ten years that self-dual Yang–Mills theory is the effective field theory of the open N=2 string in (2+2)-dimensional space–time. We uncover an infinite set of Abelian rigid string symmetries, corresponding to the symmetries and integrable hierarchy of the self-dual Yang–Mills equations. The twistor description of the latter naturally connects with the BRST approach to string quantization, providing an interpretation of the picture phenomenon in terms of the moduli space of string backgrounds.