Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-01-15
Nucl.Phys.B467:215-246,1996
Physics
High Energy Physics
High Energy Physics - Theory
50 pages, LaTeX, macros included; revised: a few missing factors of 1/2 added and two references modified; the version to appe
Scientific paper
10.1016/0550-3213(96)00088-0
We study 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, respectively. Both the N=8 and N=7 algebras admit unitary highest-weight representations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G_2, with the central charges c_8=26/5 and c_7=5, respectively. Furthermore, we show that the general coset Ans"atze for the N=8 and N=7 algebras naturally lead to the coset spaces SO(8)xU(1)/SO(7) and SO(7)xU(1)/G_2, respectively, as the additional consistent solutions for certain values of the central charge. The coset space SO(8)/SO(7) is the seven-sphere S^7, whereas the space SO(7)/G_2 represents the seven-sphere with torsion, S^7_T. The division algebra of octonions and the associated triality properties of SO(8) play an essential role in all these realizations. We also comment on some possible applications of our results to string theory.
Gunaydin Murat
Ketov Sergei V.
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