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The relaxed three-algebras: their matrix representation and implications for multi M2-brane theory

Ali Akbari, M ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1088/1126-6708/2008/12/037
  3. Publisher: 2008
  4. Abstract:
  5. We argue that one can relax the requirements of the non-associative three-algebras recently used in constructing D = 3, = 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, = 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. © 2008 SISSA
  6. Keywords:
  7. Branes ; Lie Algebra ; M-Theory
  8. Source: Journal of High Energy Physics ; Volume 2008, Issue 12 , 2008 ; 11266708 (ISSN)
  9. URL: https://iopscience.iop.org/article/10.1088/1126-6708/2008/12/037