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Paper   IPM / Physic / 8942
School of Physics
  Title:   A New Three-Algebra Representation for the N=6 su(N)Xsu(N) Superconformal Chern-Simons Theory
  Author(s):  M.M. Sheikh-Jabbari
  Status:   Published
  Journal: JHEP
  Vol.:  12
  Year:  2008
  Pages:   111
  Supported by:  IPM
  Abstract:
Based on the realization of three-algebras in terms of algebra of matrices and four-brackets [arXiv:0807.1570] we present the notion of u(N)-based extended three-algebras, which for N=2 reproduces the Bagger-Lambert three-algebra. Using these extended three-algebras we construct an su(N) su(N) Chern-Simons action with explicit SO(8) invariance. The dynamical fields of this theory are eight complex valued bosonic and fermionic fields in the bi-fundamental representation of the su(N) su(N). For generic N the fermionic transformations, however, close only on a subclass of the states of this theory onto the 3d, N=6 superalgebra. In this sector we deal with four complex valued scalars and fermions, our theory is closely related to the ABJM model [arXiv:0806.1218], and hence it can be viewed as the (low energy effective) theory of N M2-branes. We discuss that our three-algebra structure suggests a picture of open M2-brane stretched between any two pairs of M2-branes. We also analyze the BPS configurations of our model.

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