The exceptional Jordan algebra and the matrix string

2001/04/05 by Lee Smolin, Smolin, Lee · 8 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #gr-qc #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.hep-th/0104050

LaTex 15 pages, no figures

arxiv created 2001/04/05 · openalex publication_date 2001/04/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

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