Non-commutative solitons and strong-weak duality

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 $U(1){x} U(1)$ 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 $\theta$ for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG$_{1}$ $\leftrightarrow$ NCMT$_{1}$ is promising since it is expected to hold on the quantum level.Comment: 24 pages, 1 fig., LaTex. Typos in star products of eqs. (3.11)-(3.13) and footnote 1 were corrected. Version to appear in JHE

A Representation of the Virasoro Algebra via Wigner-Heisenberg Algebraic Technique to Bosonic Systems

Using the Wigner-Heisenberg algebra for bosonic systems in connection with oscillators we find a new representation for the Virasoro algebra.Comment: Revised version. Revtex, 7 pages, no figures. This work was presented in the XXII Brazilian National Meeting on Particles and Fields (October/2001), to appear in Braz. J. of Phys., 33, 1 (2003

G\"odel-type Spacetimes in Induced Matter Gravity Theory

A five-dimensional (5D) generalized G\"odel-type manifolds are examined in the light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by three essential parameters $k$, $m^2$ and $\omega$: identical triads $(k, m^2, \omega)$ correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian generalized G\"odel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that the generalized G\"odel-type 5D manifolds admit maximal group of isometry $G_r$ with $r=7$, $r=9$ or $r=15$ depending on the essential parameters $k$, $m^2$ and $\omega$. The breakdown of causality in all these classes of homogeneous G\"odel-type manifolds are also examined. It is found that in three out of the six irreducible classes the causality can be violated. The unique generalized G\"odel-type solution of the induced matter (IM) field equations is found. The question as to whether the induced matter version of general relativity is an effective therapy for these type of causal anomalies of general relativity is also discussed in connection with a recent article by Romero, Tavakol and Zalaletdinov.Comment: 19 pages, Latex, no figures. To Appear in J.Math.Phys.(1999

Division Algebras and Extended N=2,4,8 SuperKdVs

The first example of an N=8 supersymmetric extension of the KdV equation is here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It corresponds to the unique N=8 solution based on a generalized hamiltonian dynamics with (generalized) Poisson brackets given by the Non-associative N=8 Superconformal Algebra. The complete list of inequivalent classes of parametric-dependent N=3 and N=4 superKdVs obtained from the ``Non-associative N=8 SCA" is also furnished. Furthermore, a fundamental domain characterizing the class of inequivalent N=4 superKdVs based on the "minimal N=4 SCA" is given.Comment: 14 pages, LaTe

Residual Symmetries in the Presence of an EM Background

The symmetry algebra of a QFT in the presence of an external EM background (named "residual symmetry") is investigated within a Lie-algebraic, model independent scheme. Some results previously encountered in the literature are here extended. In particular we compute the symmetry algebra for a constant EM background in D=3 and D=4 dimensions. In D= 3 dimensions the residual symmetry algebra is isomorphic to $u(1)\oplus {\cal P}_c(2)$, with ${\cal P}_c(2)$ the centrally extended 2-dimensional Poincar\'e algebra. In D=4 dimension the generic residual symmetry algebra is given by a seven-dimensional solvable Lie algebra which is explicitly computed. Residual symmetry algebras are also computed for specific non-constant EM backgrounds.Comment: 11 pages, Late