International Journal of Modern Physics A

We are entering an era where a number of large-scale lattice simulations of four-dimensional supersymmetric theories are under way. Moreover, proposals for how to approach such studies continue to progress. One particular line of research in this direction is described here. General actions for super-QCD, including counterterms required on the lattice, are given. We obtain the number of fine-tunings that is required, once gauge and flavor symmetries are accounted for, provided Ginsparg–Wilson fermions are used for the gauginos. We also review and extend our recent work on lattice formulations of super-Yang–Mills and super-Yang–Mills that exploit Ginsparg–Wilson fermions.

We argue that the signals expected from the evaporation of mini black holes — predicted in TeV-gravity models with large extra dimensions, and possibly produced in ultrahigh energy collisions in the atmosphere — are quite similar to the characteristics of the Centauro events, an old mystery of cosmic-ray physics.

We consider a noncritical five-dimensional string setup which could provide a dual description of QCD in the limit of large number of colors and flavors. The model corresponds to N_c color D3-branes and N_f D4/anti-D4-brane pairs supporting flavor degrees of freedom. The matching of the string model spectrum with the dual field theory one is considered. We discuss the consequences of the possible matching of the gravity modes with the light glueballs and the interpretation of the brane spectrum in Yang–Mills and QCD.

Within the QCD factorization approach we compute the amplitudes for pure annihilation channels of B mesons decays into final states containing two pseudoscalar particles. These decays may be plagued by effects like nonperturbative physics and breaking of the factorization hypothesis and imply, at some extent, the introduction of an infrared cutoff in the calculation of amplitudes. We compute the decays with the help of infrared finite gluon propagators and coupling constants that were obtained in different solutions of the QCD Schwinger–Dyson equations. These solutions yield a natural cutoff for the amplitudes, and we argue that a systematic study of these B decays may provide a test for the QCD infrared behavior.

We demonstrate a generalization of relativistic quantum mechanics using eight-component octonic wave function and octonic spatial operators. It is shown that the second-order equation for octonic wave function describing particles with spin 1/2 can be reformulated in the form of a system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special types of wave functions the second-order equation can be reduced to the single first-order equation analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not have quantum fields.

The eigenvalues of unbounded potential from below of the form , has been obtained over a full range of the parameter values a and b. The calculated results are in complete agreement with exact numerical results obtained by H.-T. Cho and C.-L. Ho. Moreover, we also obtained analytical expression for E_n in the case when b = 0. Some new results for non-quasiexactly solvable case are presented using the asymptotic iteration method.

We investigate AdS/QCD duality for the two-point correlation function of the lowest dimension scalar glueball operator, in the case of the IR soft wall model. We point out the role of the boundary conditions for the bulk-to-boundary propagator in determining the gluon condensates. We show how a low energy QCD theorem can be obtained within the AdS approach, together with a gluon condensate close to the commonly accepted value and robust against perturbation of the background dilaton field.

The Adler–Shiota–van Moerbeke formula is employed to derive the W-constraints for the p-reduced BKP hierarchy constrained by the string equation. We also provide the Grassmannian description of the string equation in terms of the spectral parameter.

On the basis of the phenomenological relativistic harmonic models for quarks, we have obtained the masses of P-wave mesons. The full Hamiltonian used in the investigation has Lorentz scalar + vector confinement potential, along with one-gluon-exchange potential (OGEP) and the instanton-induced quark–antiquark interaction (III). A good agreement is obtained with the experimental masses. The respective role of III and OGEP for the determination of the meson masses is discussed.