2002/01/31 by Nathan Berkovits · 8 citations
Mathematics · Physics and Astronomy · #BRST quantization #Black Holes and Theoretical Physics #Combinatorics #Covariant transformation #Gauge theory #Mathematical physics #Mathematics #Nilpotent #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Pure spinor #Spinor #Superstring theory #Supersymmetry #Vertex (graph theory) #hep-th
paper · pdf · doi:10.1088/1126-6708/2002/09/051
published as JHEP 0209:051,2002 · Changed title since the hamiltonian still needs to be regularized. Added reference to Cederwall, Nilsson and Tsimpis
arxiv created 2002/04/16 · openalex publication_date 2002/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 (lambdaalpha dalpha) where dalpha is the worldvolume variable corresponding to the d=11 spacetime supersymmetric derivative and lambdaalpha is an SO(10,1) pure spinor variable satisfying (lambda Gammac 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=QL+QR is the sum of the left and right-moving Type IIA BRST operators and the eleventh component of the pure spinor constraint, (lambda Gamma11 lambda)=0, replaces the (bL0 - bR0) constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators.