Real Forms of Nonlinear Superconformal and Quasi-superconformal Algebras and Their Unified Realization

We give a complete classification of the real forms of simple nonlinear 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 nonlinear QSCA’s and SCA’s and quaternionic and superquaternionic 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-1/2 free bosons for QSCA’s and dimension-1/2 free fermions for SCA’s. The free bosons and fermions are associated with the quaternionic and superquaternionic symmetric spaces of corresponding Lie groups and Lie supergroups, respectively. We conclude with a discussion of possible applications of our results. Work supported in part by the National Science Foundation under Grant Number PHY-9631332. e-mail: [email protected]