On the equivalence of the 11D pure spinor and Brink-Schwarz-like superparticle cohomologies

Abstract

The $D=11$ pure spinor formulation of the superparticle allows a simple realization of covariant quantization, unlike the $D=11$ Brink-Schwarz-like superparticle. We explicitly show the equivalence between the cohomologies of these two models in the context of two different group decompositions: $SO(10,1)\to SO(1,1)\times SO(9)$ and $SO(10,1)\to SO(3,1)\times SO(7)$. We also carry out a light-cone analysis of the pure spinor cohomology, and show that it correctly reproduces the $SO(9)$ equations of motion for $D=11$ linearized supergravity.

24 pages. Fixed typos and added footnote

References in corpus (3)

• ICTP Lectures on Covariant Quantization of the Superstring
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach

Cited by in corpus (4)

• Systematics of the ${\alpha }^{\prime }$ Expansion in F-Theory
• Equations of motion from Cederwall's pure spinor superspace actions
• Taming the 11D pure spinor b-ghost
• Pure spinors and $D=11$ supergravity