Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory

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dc.creatorAli-Akbari, M.
dc.creatorSheikh-Jabbari, M. M.
dc.creatorSimon, J.
dc.date2008-07-10
dc.date2008-08-19
dc.date.accessioned2026-07-07T13:11:07Z
dc.date.available2026-07-07T13:11:07Z
dc.descriptionWe argue that one can relax the requirements of the non-associative three-algebras recently used in constructing D=3, N=8 superconformal field theories, and introduce the notion of ``relaxed three-algebras''. We present a specific realization of the relaxed three-algebras in terms of classical Lie algebras with a matrix representation, endowed with a non-associative four-bracket structure which is prescribed to replace the three-brackets of the three-algebras. We show that both the so(4)-based solutions as well as the cases with non-positive definite metric find a uniform description in our setting. We discuss the implications of our four-bracket representation for the D=3, N=8 and multi M2-brane theory and show that our setup can shed light on the problem of negative kinetic energy degrees of freedom of the Lorentzian case.
dc.description31 pages, no figures
dc.identifierhttps://arxiv.org/abs/0807.1570
dc.identifierhttp://arxiv.org/abs/0807.1570
dc.identifierJHEP 0812:037,2008
dc.identifierdoi:10.1088/1126-6708/2008/12/037
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229191
dc.subjectHigh Energy Physics - Theory
dc.titleRelaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory
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