On the Poincaré Superalgebra, Superspace and Supercurrents

Abstract

The Poincaré algebra can be extended to a Lie superalgebra known as the Poincaré superalgebra. Superspace provides a natural way to formulate theories invariant with respect to this bigger symmetry algebra. In this thesis, the mathematical foundations of the Poincaré superalgebra and superspace are described. We proceed to consider superspace formulations of the energy-momentum tensor and other currents. This is done by means of model-dependent realizations of current multiplets, known as supercurrents. Three current multiplets, namely the Ferrara-Zumino, R-, and S-multiplet are discussed, with examples of supercurrent realizations of these multiplets for various theories. It will shown that there are theories for which realizations of the minimal multiplets are ill-defined, and how the S-multiplet circumvents some of the issues. As a new application, a conjecture for the S-multiplet realization for the abelian gauged sigma model will be constructed.