Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-05-07
JHEP 0806:075,2008
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, Latex; small corrections and references added; published version (small typos fixed)
Scientific paper
10.1088/1126-6708/2008/06/075
We construct the totally antisymmetric structure constants f^{ABCD} of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants f^{ABCD} can be used to write down a maximally superconformal 3d theory that incorporates the expected degrees of freedom of multiple M2 branes, including the "center-of-mass" mode described by free scalar and fermion fields. The gauge field sector reduces to a three dimensional BF term, which underlies the gauge symmetry of the theory. We comment on the issue of unitarity of the quantum theory, which is problematic, despite the fact that the specific form of the interactions prevent the ghost fields from running in the internal lines of any Feynman diagram. Giving an expectation value to one of the scalar fields leads to the maximally supersymmetric 3d Yang-Mills Lagrangian with the addition of two U(1) multiplets, one of them ghost-like, which is decoupled at large g_YM.
Gomis Jaume
Milanesi Giuseppe
Russo Jorge G.
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