Hector Leny Carrion

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) ? U(1) or U(1)C corresponding to the Lechtenfeld et al. (NCSG1) or Grisaru-Penati (NCSG2) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT1,2 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 NCATM1,2 models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter ? for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG1 NCMT1 is promising since it is expected to hold on the quantum level.

Quaternionic and octonionic spinors: A Classification

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 G2 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.

Normal ordering and boundary conditions in open bosonic strings

Boundary conditions play a nontrivial role in string theory. For instance, the rich structure of D-branes is generated by choosing appropriate combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an antisymmetric background is present at the string end points (corresponding to mixed boundary conditions) space time becomes noncommutative there. We show here how to build up normal ordered products for bosonic string position operators that satisfy both equations of motion and open string boundary conditions at the quantum level. We also calculate the equal time commutator of these normal ordered products in the presence of an antisymmetric tensor background.

OCTONIONIC REALIZATIONS OF ONE-DIMENSIONAL EXTENDED SUPERSYMMETRIES: A CLASSIFICATION

The classification of the octonionic realizations of the one-dimensional extended supersymmetries is here furnished. These are non-associative realizations which, albeit inequivalent, are put in correspondence with a subclass of the already classified associative representations for 1D extended supersymmetries. Examples of dynamical systems invariant under octonionic realizations of the extended supersymmetries are given. We cite among the others the octonionic spinning particles, the N=8 KdV, etc. Possible applications to supersymmetric systems arising from dimensional reduction of the octonionic superstring and M-theory are mentioned.

LIE 3-ALGEBRA AND SUPER-AFFINIZATION OF SPLIT-OCTONIONS

The purpose of this study is to extend the concept of a generalized Lie 3-algebra, known to the divisional algebra of the octonions 𝕆, to split-octonions 𝕊𝕆, which is non-divisional. This is achieved through the unification of the product of both of the algebras in a single operation. Accordingly, a notational device is introduced to unify the product of both algebras. We verify that 𝕊𝕆 is a Malcev algebra and we recalculate known relations for the structure constants in terms of the introduced structure tensor. Finally we construct the manifestly supersymmetric

Some comments on the integrability of the noncommutative generalized massive Thirring model

\mathcal{N} = 1{\mathbb SO}

RESIDUAL SYMMETRIES IN THE PRESENCE OF AN EM BACKGROUND

affine superalgebra. An application of the split Lie 3-algebra for a Bagger and Lambert gauge theory is also discussed.

Octonionic Realizations of One-Dimensional Extended Supersymmetries

Some properties of a non-commutative version of the generalized massive Thirring theory (NCGMT) are studied. We develop explicit calculations for the affine Lie algebra

Classical strings in Ad{S_4} {C}{{P}^3} with three angular momenta

gl(3)

Noncommmutative solitons and kinks in the affine Toda model coupled to matter

case. The NCGMT model is written in terms of Dirac type fields corresponding to the Moyal product extension of the ordinary multi-field massive Thirring model. We discuss the Lagrangian formulation, its zero-curvature representation and integrability property of certain submodels.