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
SN - 0920-5632
VL - 56
SP - 70
EP - 75
JO - Nuclear Physics B - Proceedings Supplements
JF - Nuclear Physics B - Proceedings Supplements
IS - 3
ER -