Real forms of nonlinear superconformal and quasi-superconformal algebras and their unified realization

Abstract

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.

A paragraph together with a few new references added. Version to appear in Nuclear Physics B. 36 pages, latex file

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• Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
• A Unified Approach to the Minimal Unitary Realizations of Noncompact Groups and Supergroups
• Higher Spin Currents in Wolf Space: Part I
• Minimal realization of $\ell$-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation
• Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• Dual Theory for maximally $\mathcal{N}$ extended flat Supergravity
• On the Classification of Real Forms of Non-Abelian Toda Theories and W-algebras
• SU(1,2) invariance in two-dimensional oscillator
• Hidden symmetries of deformed oscillators
• Oscillators from nonlinear realizations