Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization Original Research Article

We give a complete classification of the real forms of simple non-linear superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and present a unified realization of these algebras with simple symmetry groups. This classification is achieved by establishing a correspondence between simple non-linear QSCAʹs and SCAʹs and quaternionic and super-quaternionic symmetric spaces of simple Lie groups and Lie supergroups, respectively. The unified realization we present involves a dimension zero scalar field (dilaton), dimension-1 symmetry currents, and dimension-12 free bosons for QSCAʹs and dimension-case12 free fermions for SCAʹs. The free bosons and fermions are associated with the quaternionic and super-quaternionic symmetric spaces of corresponding Lie groups and Lie supergroups, respectively. We conclude with a discussion of possible applications of our results.