Three-algebra for supermembrane and two-algebra for superstring

Details Three-algebra for supermembrane and two-algebra for superstring Three-algebra for supermembrane and two-algebra for superstring

2009-02-14

arxiv.org/abs/0902.2417v2

JHEP 0904:012,2009

Physics

High Energy Physics

High Energy Physics - Theory

1+15 pages, no figure; Refs added, Accepted for publication in JHEP

Scientific paper

10.1088/1126-6708/2009/04/012

While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in eleven dimensions, which is invariant under global supersymmetry, local fermionic symmetry and worldvolume diffeomorphism. Our action is classically on-shell equivalent to the celebrated Bergshoeff-Sezgin-Townsend action. However, the novelty is that we spell the action genuinely in terms of Nambu three-brackets: All the derivatives appear through Nambu brackets and hence it manifests the three-algebra structure. Further the double dimensional reduction of our action gives straightforwardly to a type IIA string action featuring two-algebra. Applying the same method, we also construct a covariant action for type IIB superstring, leading directly to the IKKT matrix model.

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