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

TL;DR

This paper classifies all real forms of nonlinear superconformal and quasi-superconformal algebras, providing a unified realization linked to quaternionic symmetric spaces, with potential applications in theoretical physics.

Contribution

It offers a complete classification of real forms of nonlinear SCA and QSCA and introduces a unified realization based on symmetric spaces and simple symmetry groups.

Findings

Classification of all real forms of nonlinear SCA and QSCA

Unified realization involving symmetry groups and symmetric spaces

Connection between algebra structures and geometric symmetric spaces

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.