Pure Spinors, Free Differential Algebras, and the Supermembrane

Abstract

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.

arXiv comment38 pp. Latex

References in corpus (29)

• Super-Poincare Covariant Quantization of the Superstring
• Black and super p-branes in diverse dimensions
• Ten-Dimensional Supergravity Constraints from the Pure Spinor Formalism for the Superstring
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• Superpotentials and Membrane Instantons
• Towards Covariant Quantization of the Supermembrane
• Covariant Quantization of Superstrings Without Pure Spinor Constraints
• Covariant One-Loop Amplitudes in D=11
• On the Berkovits Covariant Quantization of GS Superstring
• The Superembedding Origin of the Berkovits Pure Spinor Covariant Quantization of Superstrings
• Origin of Pure Spinor Superstring
• Twisted N=2 Supergravity as Topological Gravity in Four Dimensions
• A k Gauge Fixed Type IIB Superstring Action on AdS_{5} X S_{5}
• The Covariant Quantum Superstring and Superparticle from their Classical Actions
• On the formulation of D=11 supergravity and the composite nature of its three-from field
• The Quantum Superstring as a WZNW Model with N=2 Superconformal Symmetry
• The Osp(8|4) singleton action from the supermembrane
• Four-Point One-Loop Amplitude Computation in the Pure Spinor Formalism
• The 0-brane action in a general D=4 supergravity background
• Gauging Cosets
• Nondegenerate Super-Anti-de Sitter Algebra and a Superstring Action
• Generalized curvature and the equations of D=11 supergravity
• Super D-branes from BRST Symmetry
• Vertex Operators for the Supermembrane and Background Field Matrix Theory
• M-theory FDA, Twisted Tori and Chevalley Cohomology
• A new first order formalism for k-supersymmetric Born Infeld actions: the D3-brane example
• Lie derivatives along antisymmetric tensors, and the M-theory superalgebra
• Extended Lie derivatives and a new formulation of D=11 supergravity
• An SL(2,R)-covariant, first order, k-supersymmetric action for the D5-brane

Cited by in corpus (13)

• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• Pure spinor superfields -- an overview
• Superstrings on AdS_4 x CP^3 from Supergravity
• Explaining Pure Spinor Superspace
• The cohomology of superspace, pure spinors and invariant integrals
• Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds
• Free Differential Algebras, Rheonomy, and Pure Spinors
• Pure Spinor Approach to Type IIA Superstring Sigma Models and Free Differential Algebras
• Constrained Supermanifolds for AdS M-Theory Backgrounds
• Towards relating the kappa-symmetric and pure-spinor versions of the supermembrane
• Pure Spinors for General Backgrounds
• Free Differential Algebras and Pure Spinor Action in IIB Superstring Sigma Models
• Non-commutative M-branes from Open Pure Spinor Supermembrane