Pure Spinors, Free Differential Algebras, and the Supermembrane

Details Pure Spinors, Free Differential Algebras, and the Supermembrane Pure Spinors, Free Differential Algebras, and the Supermembrane

2006-06-19

arxiv.org/abs/hep-th/0606171v1

Nucl.Phys.B763:1-34,2007

Physics

High Energy Physics

High Energy Physics - Theory

38 pp. Latex

Scientific paper

10.1016/j.nuclphysb.2006.10.026

The lagrangian formalism for the supermembrane in any 11d supergravity background is constructed in the pure spinor framework. Our gauge-fixed action is manifestly BRST, supersymmetric, and 3d Lorentz invariant. The relation between the Free Differential Algebras (FDA) underlying 11d supergravity and the BRST symmetry of the membrane action is exploited. The "gauge-fixing" has a natural interpretation as the variation of the Chevalley cohomology class needed for the extension of 11d super-Poincare' superalgebra to M-theory FDA. We study the solution of the pure spinor constraints in full detail.

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