3 research outputs found
Exceptional Superconformal Algebras
Reductive W-algebras which are generated by bosonic fields of spin-1, a
single spin-2 field and fermionic fields of spin-3/2 are classified. Three new
cases are found: a `symplectic' family of superconformal algebras which are
extended by , an and an superconformal algebra.
The exceptional cases can be viewed as arising a Drinfeld-Sokolov type
reduction of the exceptional Lie superalgebras and , and have an
octonionic description. The quantum versions of the superconformal algebras are
constructed explicitly in all three cases.Comment: 16 page
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 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.Comment: A paragraph together with a few new references added. Version to
appear in Nuclear Physics B. 36 pages, latex fil