Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization

Behzad Bina, Murat Günaydin

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We give a complete classification of the real forms of simple non-linear 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 non-linear QSCA's and SCA's and quaternionic and super-quaternionic symmetric spaces of simple Lie groups and Lie supergroups, respectively. The unified realization we present involves a dimension zero scalar field (dilaton), dimension-1 symmetry currents, and dimension-1/2 free bosons for QSCA's and dimension-1/2 free fermions for SCA's. The 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.

Original languageEnglish (US)
Pages (from-to)713-740
Number of pages28
JournalNuclear Physics B
Volume502
Issue number3
DOIs
StatePublished - Oct 6 1997

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algebra
bosons
fermions
symmetry
scalars

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Cite this

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abstract = "We give a complete classification of the real forms of simple non-linear 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 non-linear QSCA's and SCA's and quaternionic and super-quaternionic symmetric spaces of simple Lie groups and Lie supergroups, respectively. The unified realization we present involves a dimension zero scalar field (dilaton), dimension-1 symmetry currents, and dimension-1/2 free bosons for QSCA's and dimension-1/2 free fermions for SCA's. The 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.",
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Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization. / Bina, Behzad; Günaydin, Murat.

In: Nuclear Physics B, Vol. 502, No. 3, 06.10.1997, p. 713-740.

Research output: Contribution to journalArticle

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