Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-03-26
Nucl.Phys.B502:713-740,1997
Physics
High Energy Physics
High Energy Physics - Theory
A paragraph together with a few new references added. Version to appear in Nuclear Physics B. 36 pages, latex file
Scientific paper
10.1016/S0550-3213(97)00406-9
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 super-quaternionic symmetric spaces of simple Lie groups and Lie supergroups, respectively. The unified realization involves a dimension zero boson (dilaton), dimension one symmetry currents and dimension 1/2 free bosons for QSCA'a and dimension 1/2 free fermions for SCA's. The dimension 1/2 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.
Bina Behzad
Gunaydin Murat
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