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

M. Ali-Akbari, M. M. Sheikh-Jabbari, J. Simon

Research output: Contribution to journalArticlepeer-review

Abstract

We 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.
Original languageEnglish
Number of pages26
JournalJournal of High Energy Physics
Volume2008
Issue number12
DOIs
Publication statusPublished - 10 Jul 2008

Keywords

  • hep-th
  • M-Theory
  • AdS-CFT and dS-CFT Correspondence

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