Actions for two-superparticle system in (10,2) dimensions and three-superparticle systems in (11,3) dimensions are constructed. These actions have worldline bosonic and fermionic local symmetries, and target space global supersymmety generalizing the reparametrization, kappa-symmetry and Poincare supersymmetry of the usual superparticle. With the second particle, or the second and third particles on-shell, they describe a superparticle propagating in the background of a second superparticle in (10,2) dimensions, or two other superparticles in (11,3) dimensions. Symmetries of the action are shown to exist in presence of super Yang-Mills background as well.Comment: 12 pages, latex, replaced Note Added to appear as an Addendu

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Spacetime superalgebras with 64 or less number of real supercharges, containing the type IIB Poincaré superalgebra in (9, 1) dimensions and the N = 1 Poincaré superalgebra in (10, 1) are considered. The restriction D ≤ 14, and two distinct possibilities arise: The N = (1, 0) superalgebra in (11, 3) dimensions, and the N = (2, 0) superalgebra in (10, 2) dimensions. Emphasizing the former, we describe superparticle and super Yang-Mills systems in (11, 3) dimensions. We also propose an N = (2, 1) superstring theory in (n, n) dimensions as a possible origin of super Yang-Mills in (8 + n, n) dimensions.

The superembedding approach to p-branes is used to study a class of p-branes which have linear multiplets on the worldvolume. We refer to these branes as L-branes. Although linear multiplets are related to scalar multiplets (with 4 or 8 supersymmetries) by dualising one of the scalars of the latter to a p-form field strength, in many geometrical situations it is the linear multiplet version which arises naturally. Furthermore, in the case of 8 supersymmetries, the linear multiplet is off-shell in contrast to the scalar multiplet. The dynamics of an L-brane are obtained by using a systematic procedure for constructing the Green-Schwarz action from the superembedding formalism. This action has a Dirac-Born-Infeld type structure for the p-form. In addition, a set of equations of motion is postulated directly in superspace, and is shown to agree with the Green-Schwarz equations of motion. †

A model for n superparticles in (d − n, n) dimensions is studied. The target space supersymmetry involves a product of n momentum generators, and the action has n(n + 1)/2 local bosonic symmetries and n local fermionic symmetries. The precise relation between the symmetries presented here and those existing in the literature is explained. A new model is proposed for superparticles in arbitrary dimensions where coordinates are associated with all the p-form charges occuring in the superalgebra. The model naturally gives rise to the BPS condition for the charges.