Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-10-21
JHEP 0812:111,2008
Physics
High Energy Physics
High Energy Physics - Theory
39 pages, 3 .eps figures, v2: References added, typos corrected, v3: typos corrected, an appendix added, the version to appear
Scientific paper
10.1088/1126-6708/2008/12/111
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)\times 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)\times su(N). For generic N the fermionic transformations, however, close only on a subclass of the states of this theory onto the 3d, {\cal 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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