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 language | English |
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Number of pages | 26 |
Journal | Journal of High Energy Physics |
Volume | 2008 |
Issue number | 12 |
DOIs | |
Publication status | Published - 10 Jul 2008 |
Keywords / Materials (for Non-textual outputs)
- hep-th
- M-Theory
- AdS-CFT and dS-CFT Correspondence