TY - JOUR
T1 - Ternary algebraic approach to extended superconformal algebras
AU - Günaydin, Murat
AU - Hyun, Seungjoon
N1 - Funding Information:
* Work supported in part by the National Science Foundation under Grant PHY-8909549.
PY - 1992/4/13
Y1 - 1992/4/13
N2 - The construction of extended (N = 2 and N = 4) superconformal algebras (SCA) over very general classes of ternary algebras (triple systems) is given. For N = 2 this construction leads to superconformal algebras corresponding to certain Kählerian coset spaces of Lie groups with non-vanishing torsion. In general, a given Lie group admits more than one coset space of this type. The construction and a complete classification of N = 2 SCAs over Kantor triple system is given. In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the coset spaces of the groups of the Magic Square. For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU(2)×SU(2)×U(1). The realization and a complete classification of N = 2 and N = 4.
AB - The construction of extended (N = 2 and N = 4) superconformal algebras (SCA) over very general classes of ternary algebras (triple systems) is given. For N = 2 this construction leads to superconformal algebras corresponding to certain Kählerian coset spaces of Lie groups with non-vanishing torsion. In general, a given Lie group admits more than one coset space of this type. The construction and a complete classification of N = 2 SCAs over Kantor triple system is given. In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the coset spaces of the groups of the Magic Square. For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU(2)×SU(2)×U(1). The realization and a complete classification of N = 2 and N = 4.
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U2 - 10.1016/0550-3213(92)90271-C
DO - 10.1016/0550-3213(92)90271-C
M3 - Article
AN - SCOPUS:0000523809
SN - 0550-3213
VL - 373
SP - 688
EP - 712
JO - Nuclear Physics, Section B
JF - Nuclear Physics, Section B
IS - 3
ER -