Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-05-26
JHEP0807:136,2008
Physics
High Energy Physics
High Energy Physics - Theory
v3: Appendix A added proving an identity; minor corrections and typos fixed. v4: slight refinement in section 2.1, no other ch
Scientific paper
10.1088/1126-6708/2008/07/136
We study the 3-algebraic structure involved in the recently shown M2-branes worldvolume gauge theories. We first extend an arbitrary finite dimensional 3-algebra into an infinite dimensional 3-algebra by adding a mode number to each generator. A unique central charge in the algebra of gauge transformations appears naturally in this extension. We present an infinite dimensional extended 3-algebra with a general metric and also a different extension with a Lorentzian metric. We then study ordinary finite dimensional 3-algebras with different signatures of the metric, focusing on the cases with a negative eigenvalue and the cases with a zero eigenvalue. In the latter cases we present a new algebra, whose corresponding theory is a decoupled abelian gauge theory together with a free theory with global gauge symmetry, and there is no negative kinetic term from this algebra.
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