From Superalgebras to Superparticles and Superbranes

Abstract

In this work we investigate connections between superalgebras and their realizations in terms of particles, branes and field theory models. We start from Poincar\'e superalgebras with brane charges and study its representations. The existence of new supermultiplets in different dimensions including an ultra short supermultiplet in D=11 different from the supergravity multiplet is shown. Generalizations of superalgebras containing brane charges, including those in D$>$11 are considered. The realization of these algebras at the level of relativistic particle models and, upon quantization, at the level of field theory is presented. Application of Hamiltonian/BRST methods of quantization of systems with mixture of first and second class constraints as well as a conversion method are discussed for the models of interest. Using quantization of particle mechanics we obtain information on the spectrum and linearized equations of motion of the perturbative, linearized M-theory. The generalization of particle models to p-branes is made using a geometrical formulation of superembedding approach to study the example of L-branes which have a linear multiplet on their worldvolume. The p-branes and strings in B-field are considered as well as the origin of noncommutativity and non-associativity in their low-energy limit. It is shown that the application of Hamiltonian/BRST methods for those models leads to stringy version of Seiberg-Witten map and the removal of the non-associativity/noncommutativity.