Towards Covariant Quantization of the Supermembrane

TL;DR

This paper extends covariant quantization methods to the eleven-dimensional supermembrane using pure spinors, constructing vertex operators and proposing a framework for M-theory scattering amplitudes.

Contribution

It introduces a covariant quantization formalism for the supermembrane with pure spinors and constructs explicit vertex operators in this framework.

Findings

Constructed supermembrane vertex operators in BRST cohomology.

Related supermembrane operators to Type IIA superstring operators.

Proposed a conjecture for M-theory scattering amplitude computation.

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.