Towards Covariant Quantization of the Supermembrane

Abstract

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q=int (lambda^alpha d_alpha) where d_alpha is the worldvolume variable corresponding to the d=11 spacetime supersymmetric derivative and lambda^alpha is an SO(10,1) pure spinor variable satisfying (lambda Gamma^c lambda)=0 for c=1 to 11. Super-Poincare covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to Type IIA superstring vertex operators where Q=Q_L+Q_R is the sum of the left and right-moving Type IIA BRST operators and the eleventh component of the pure spinor constraint, (lambda Gamma^{11} lambda)=0, replaces the (b_L^0 - b_R^0) constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators.

Changed title since the hamiltonian still needs to be regularized. Added reference to Cederwall, Nilsson and Tsimpis

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Cited by in corpus (71)

• ICTP Lectures on Covariant Quantization of the Superstring
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• Covariant One-Loop Amplitudes in D=11
• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring
• Origin of Pure Spinor Superstring
• Vertex Operators for Closed Superstrings
• Pure spinor superfields -- an overview
• A New First Class Algebra, Homological Perturbation and Extension of Pure Spinor Formalism for Superstring
• The Covariant Quantum Superstring and Superparticle from their Classical Actions
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
• The Character of Pure Spinors
• On higher-order corrections in M theory
• Towards a manifestly supersymmetric action for 11-dimensional supergravity
• Ghost constraints and the covariant quantization of the superparticle in ten dimensions
• Systematics of the ${\alpha }^{\prime }$ Expansion in F-Theory
• GGI Lectures on the Pure Spinor Formalism of the Superstring
• Curved 11D Supergeometry
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• Explaining Pure Spinor Superspace
• Relating Green-Schwarz and Extended Pure Spinor Formalisms by Similarity Transformation
• Higher-derivative gauge field terms in the M-theory action
• Operator Mapping between RNS and Extended Pure Spinor Formalisms for Superstring
• Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach
• The cohomology of superspace, pure spinors and invariant integrals
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• Covariant Multiloop Superstring Amplitudes
• Quantum Field Theory as Effective BV Theory from Chern-Simons
• Equations of motion from Cederwall's pure spinor superspace actions
• Notes on the ambitwistor pure spinor string
• Pure-spinor superstrings in d=2,4,6
• Perspectives on the pure spinor superfield formalism
• Maximally twisted eleven-dimensional supergravity
• Membranes for Topological M-Theory
• Pure Spinors, Free Differential Algebras, and the Supermembrane
• Noncommutative Supersymmetric/Integrable Models and String Theory
• Supersymmetric S-matrices from the worldsheet in 10 and 11d
• Super D-branes from BRST Symmetry
• Simplified D=11 Pure Spinor b Ghost
• The geometry of pure spinor space
• On the equivalence of the 11D pure spinor and Brink-Schwarz-like superparticle cohomologies
• Notes on the $D=11$ pure spinor superparticle
• N=2 Superparticles, RR Fields and Noncommutative Structures of (super)-Spacetime
• Ultraviolet divergences in maximal supergravity from a pure spinor point of view
• Pure Spinor Approach to Type IIA Superstring Sigma Models and Free Differential Algebras
• Constrained Supermanifolds for AdS M-Theory Backgrounds
• N=4 Superconformal Symmetry for the Covariant Quantum Superstring
• The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity
• Towards relating the kappa-symmetric and pure-spinor versions of the supermembrane
• D-branes from Pure Spinor Superstring in AdS_5 x S^5 Background
• Note About Redefinition of BRST Operator for Pure Spinor String in General Background
• Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravity
• Geometry of a desingularization of eleven-dimensional gravitational spinors
• Pure spinor formulation of the superstring and its applications
• The quantum algebra of superspace
• Free Differential Algebras and Pure Spinor Action in IIB Superstring Sigma Models
• Non-BPS D-Branes in Light-Cone Green-Schwarz Formalism
• Taming the 11D pure spinor b-ghost
• Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. I
• Surface Operators in Superspace
• Spin Cohomology
• On the construction of integrated vertex in the pure spinor formalism in curved background
• Six-dimensional supermultiplets from bundles on projective spaces
• The Derived Pure Spinor Formalism as an Equivalence of Categories
• Non-commutative M-branes from Open Pure Spinor Supermembrane
• Pure spinors and $D=11$ supergravity
• Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. II
• Origin of the Pure Spinor and Green-Schwarz Formalisms
• Supersymmetric String Configurations in Ad${\mathbb{S}}_5\times {\mathbb{S}}^5$
• Towards Pure Spinor Type Covariant Description of Supermembrane -- An Approach from the Double Spinor Formalism --
• Homotopy representations of extended holomorphic symmetry in holomorphic twists