Ternary algebraic approach to extended superconformal algebras

Murat Günaydin, Seungjoon Hyun

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)688-712
Number of pages25
JournalNuclear Physics, Section B
Volume373
Issue number3
DOIs
StatePublished - Apr 13 1992

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algebra
division
torsion
tensors
products

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Cite this

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abstract = "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 K{\"a}hlerian 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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Ternary algebraic approach to extended superconformal algebras. / Günaydin, Murat; Hyun, Seungjoon.

In: Nuclear Physics, Section B, Vol. 373, No. 3, 13.04.1992, p. 688-712.

Research output: Contribution to journalArticle

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