TY - JOUR

T1 - Seven-sphere and the exceptional N = 7 and N = 8 superconformal algebras

AU - Günaydin, Murat

AU - Ketov, Sergei V.

N1 - Funding Information:
I E-mail: murat@phys.psu.edu 2 E-mail: ketov@itp.uni-hannover.de 3 Supported in part by the 'Deutsche Forschungsgemeinschaft' and the 'Volkswagen Stiftung'. 4 On leave of absence from: High Current Electronics Institute of the Russian Academy of Sciences, Siberian Branch, Akademichesky 4, Tomsk 634055, Russia.

PY - 1996/5/13

Y1 - 1996/5/13

N2 - We study realisations 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 highest-weight 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, respectively. Furthermore, we show that the general coset ansätze for the N = 8 and N = 7 algebras naturally lead to the coset spaces SO(8) × U(1)/SO(7) and SO(7) × U(1)/G2, respectively, as the additional consistent solutions for certain values of the central charge. The coset space SO(8)/SO(7) is the seven-sphere S7, whereas the space SO(7)/G2 represents the seven-sphere with torsion, S7T. The division algebra of octonions and the associated triality properties of SO(8) play an essential role in all these realisations. We also comment on some possible applications of our results to string theory.

AB - We study realisations 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 highest-weight 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, respectively. Furthermore, we show that the general coset ansätze for the N = 8 and N = 7 algebras naturally lead to the coset spaces SO(8) × U(1)/SO(7) and SO(7) × U(1)/G2, respectively, as the additional consistent solutions for certain values of the central charge. The coset space SO(8)/SO(7) is the seven-sphere S7, whereas the space SO(7)/G2 represents the seven-sphere with torsion, S7T. The division algebra of octonions and the associated triality properties of SO(8) play an essential role in all these realisations. We also comment on some possible applications of our results to string theory.

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U2 - 10.1016/0550-3213(96)00088-0

DO - 10.1016/0550-3213(96)00088-0

M3 - Article

AN - SCOPUS:0030582003

VL - 467

SP - 215

EP - 246

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -