Letters in Mathematical Physics

, Volume 19, Issue 1, pp 65–71

Nonstandard signature of spacetime, superstrings, and the split composition algebras

  • R. Foot
  • G. C. Joshi

DOI: 10.1007/BF00402262

Cite this article as:
Foot, R. & Joshi, G.C. Lett Math Phys (1990) 19: 65. doi:10.1007/BF00402262


It has been established that the covering group of the Lorentz group in the dimensions D=3, 4, 6 and 10, can be expressed in a unified way, based on the four composition-division algebras ℝ, ℂ, ℚ and \(\mathbb{O}\). If the division algebras in the construction of the covering groups of the Lorentz groups in D=3, 4, 6 and 10 are replaced by the split composition algebras, then the sequence of groups \(\widetilde{{\text{SO}}}{\text{(2,2)}}\), \(\widetilde{{\text{SO}}}{\text{(3,3)}}\) and \(\widetilde{{\text{SO}}}{\text{(5,5)}}\) results. Classical superstrings embedded in such spacetimes can be defined, and the split composition algebras provide a natural framework for their description.

AMS subject classification (1980)


Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • R. Foot
    • 1
  • G. C. Joshi
    • 1
  1. 1.Research Centre for High Energy Physics, School of PhysicsUniversity of MelbourneParkvilleAustralia