The exceptional Jordan algebra and the matrix string

Abstract

A new matrix model is described, based on the exceptional Jordan algebra. The action is cubic, as in matrix Chern-Simons theory. We describe a compactification that, we argue, reproduces, at the one loop level, an octonionic compactification of the matrix string theory in which SO(8) is broken to G2. There are 27 matrix degrees of freedom, which under Spin(8) transform as the vector, spinor and conjugate spinor, plus three singlets, which represent the two longitudinal coordinates plus an eleventh coordinate. Supersymmetry appears to be related to triality of the representations of Spin(8).

LaTex 15 pages, no figures

References in corpus (7)

• Matrix String Theory
• Proposals on nonperturbative superstring interactions
• The geometry of three-forms in six and seven dimensions
• Finite Lorentz Transformations, Automorphisms, and Division Algebras
• Dual formulation of spin network evolution
• Dimensional Reduction
• Holography in a quantum spacetime

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