TY - JOUR

T1 - Seven sphere and the exceptional nonlinear superconformal algebras

AU - Günaydin, Murat

N1 - Funding Information:
part by the National Science Founda-Grant No. PHY-9631332 0920-5632/97/$17.00 Q 1997 Elsevier Science B.V. All rights reserved. PII: SO920-5632(97)003 1 l-3

PY - 1997/7

Y1 - 1997/7

N2 - 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 S7, 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.

AB - 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 S7, 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.

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U2 - 10.1016/S0920-5632(97)00311-3

DO - 10.1016/S0920-5632(97)00311-3

M3 - Article

AN - SCOPUS:0031187971

VL - 56

SP - 70

EP - 75

JO - Nuclear and Particle Physics Proceedings

JF - Nuclear and Particle Physics Proceedings

SN - 2405-6014

IS - 3

ER -