Seven Sphere and the Exceptional Nonlinear Superconformal Algebras
نویسنده
چکیده
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 S, 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. 1Work supported in part by the National Science Foundation under research Grant No. PHY-9631332. email: [email protected]
منابع مشابه
Seven–sphere and the Exceptional N=7 and N=8 Superconformal Algebras
We study 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, respectively. Both the N = 8 and N = 7 algebras admit unitary highestweight representations 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, respectiv...
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