Seven sphere and the exceptional nonlinear superconformal algebras

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The realizations of the exceptional non-linear (quadratically generated, or W-type) N = 8 and N = 7 superconformal algebras with Spin(7) and G2 affine symmetry currents are reviewed. Both the N = 8 and N = 7 algebras admit unitary realizations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G2, with the central charges c8 = 26/5 and c7 = 5, respectively. They can also be realized over the coset spaces SO(8) × U(1)/SO(7) and SO(7) × U(1)/G2 for some fixed values of their central charges, respectively. The coset space SO(8)/SO(7) is the seven-sphere S7, whereas the space SO(7)/G2 represents the seven-sphere with torsion. We conclude with a discussion of a novel 'hybrid' method developed recently that yields unitary realizations of the exceptional N = 8 and N = 7 algebras for all allowed values of their central charges.

Original languageEnglish (US)
Pages (from-to)70-75
Number of pages6
JournalNuclear Physics B - Proceedings Supplements
Issue number3
StatePublished - Jul 1997

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics


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