Seven Sphere and the Exceptional Nonlinear Superconformal Algebras

Details Seven Sphere and the Exceptional Nonlinear Superconformal Algebras Seven Sphere and the Exceptional Nonlinear Superconformal Algebras

1997-03-03

arxiv.org/abs/hep-th/9703021v1

Nucl.Phys.Proc.Suppl.56B:70-75,1997

Physics

High Energy Physics

High Energy Physics - Theory

Talk given at the 30th International Symposium on the Theory of Elementary Particles, Buckow, Germany (Aug. 27-31, 1996). 11 p

Scientific paper

10.1016/S0920-5632(97)00311-3

The realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 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 G_2, with the central charges c=26/5 and c=5, respectively. They also have realizations over the coset spaces SO(8)XU(1)/SO(7) and SO(7)X U(1)/G_2 for some fixed values of their central charges. The coset space SO(8)/SO(7) is the seven-sphere , whereas the space SO(7)/G_2 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.

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