REAL FORMS OF NONLINEAR SUPERCONFORMAL AND QUASI-SUPERCONFORMAL ALGEBRAS AND THEIR UNIFIED REALIZATION

We give a complete classification of the real forms of simple non-line ar superconformal algebras (SCA) and quasi-superconformal algebras (QS CA) and present a unified realization of these algebras with simple sy mmetry groups, This classification is achieved by establishing a corre spondence between simple non-linear QSCA's and SCA's and quaternionic and super-quaternionic symmetric spaces of simple Lie groups and Lie s upergroups, respectively. The unified realization we present involves a dimension zero scalar field (dilaton), dimension-1 symmetry currents , and dimension-1/2 free bosons for QSCA's and dimension-1/2 free ferm ions for SCA's. The free bosons and fermions are associated with the q uaternionic and super-quaternionic symmetric spaces of corresponding L ie groups and Lie supergroups, respectively. We conclude with a discus sion of possible applications of our results. (C) 1997 Elsevier Scienc e B.V.