The spectrum of light baryons and mesons has been reproduced recently by Brodsky and Teramond from a holographic dual to QCD inspired in the AdS/CFT correspondence. They associate fluctuations about the AdS geometry with four dimensional angular momenta of the dual QCD states. We use a similar approach to estimate masses of glueball states with different spins and their excitations. We consider Dirichlet and Neumann boundary conditions and find approximate linear Regge trajectories for these glueballs. In particular the Neumann case is consistent with the Pomeron trajectory.

Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and octonionic spinors is presented. In the octonionic case we further provide a systematic list of results and tables expressing, e.g., the relations of the octonionic Clifford algebras with the G 2 cosets over the Lorentz algebras, the identities satisfied by the higher-rank antisymmetric octonionic tensors and so on. Applications of these results range from the classification of octonionic generalized supersymmetries, the construction of octonionic superstrings, as well as the investigations concerning the recently discovered octonionic M-superalgebra and its superconformal extension.

Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either U (1)xU (1) or U (1) C corresponding to the Lechtenfeld et al. (NCSG 1 ) or Grisaru-Penati (NCSG 2 ) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT 1,2 models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM 1,2 models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter θ for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG 1 ↔ NCMT 1 is promising since it is expected to hold on the quantum level. * ⋆ e −iϕ + ⋆ − 2 .(3.11)In this way we have re-derived the Lechtenfeld et al. action (NCSG 1

The solitons and kinks of the generalized sl(3,C) sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the tau functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the sl(3,C) affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized sl(3,C) sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U (1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for "quark" confinement.