The Seven-sphere and its Kac-Moody Algebra
High Energy Physics - Theory
2009-10-22 v1 alg-geom
Quantum Algebra
Abstract
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 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.
Keywords
Cite
@article{arxiv.hep-th/9309030,
title = {The Seven-sphere and its Kac-Moody Algebra},
author = {Martin Cederwall and Christian R. Preitschopf},
journal= {arXiv preprint arXiv:hep-th/9309030},
year = {2009}
}
Comments
22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appended