The Seven-sphere and its Kac-Moody Algebra

Details The Seven-sphere and its Kac-Moody Algebra The Seven-sphere and its Kac-Moody Algebra

1993-09-06

arxiv.org/abs/hep-th/9309030v1

Commun.Math.Phys. 167 (1995) 373-394

Physics

High Energy Physics

High Energy Physics - Theory

22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appended

Scientific paper

10.1007/BF02100591

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under $S^7$ are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given.

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