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Paper IPM / P / 8942  


Abstract:  
Based on the realization of threealgebras in terms of algebra of matrices and fourbrackets [arXiv:0807.1570] we present the notion of u(N)based extended threealgebras, which for N=2 reproduces the BaggerLambert threealgebra. Using these extended threealgebras we construct an su(N) su(N) ChernSimons action with explicit SO(8) invariance. The dynamical fields of this theory are eight complex valued bosonic and fermionic fields in the bifundamental 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 M2branes. We discuss that our threealgebra structure suggests a picture of open M2brane stretched between any two pairs of M2branes. We also analyze the BPS configurations of our model.
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