### Abstract

We study realisations 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 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)/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 realisations. We also comment on some possible applications of our results to string theory.

Original language | English |
---|---|

Pages (from-to) | 215-246 |

Number of pages | 32 |

Journal | Nuclear Physics B |

Volume | 467 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 13 May 1996 |

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### Keywords

- Conformal field theory
- Seven sphere
- String theory
- Superconformal symmetry
- Triality

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*467*(1-2), 215-246. https://doi.org/10.1016/0550-3213(96)00088-0

**Seven-sphere and the exceptional N = 7 and N = 8 superconformal algebras.** / Günaydin, Murat; Ketov, Sergei V.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 467, no. 1-2, pp. 215-246. https://doi.org/10.1016/0550-3213(96)00088-0

}

TY - JOUR

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

AU - Günaydin, Murat

AU - Ketov, Sergei V.

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.

KW - Conformal field theory

KW - Seven sphere

KW - String theory

KW - Superconformal symmetry

KW - Triality

UR - http://www.scopus.com/inward/record.url?scp=0030582003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030582003&partnerID=8YFLogxK

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

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

M3 - Article

VL - 467

SP - 215

EP - 246

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -