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Paper   IPM / Physic / 8907
School of Physics
  Title:   The Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory
1.  M. Ali-Akbari
2.  M.M. Sheikh-Jabbari
3.  J. Simon
  Status:   Published
  Journal: JHEP
  Vol.:  12
  Year:  2008
  Pages:   037
  Supported by:  IPM
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.

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