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

## TL;DR

This paper demonstrates the equivalence of cohomologies between the pure spinor and Brink-Schwarz-like superparticle models in 11 dimensions, providing insights into covariant quantization and supergravity equations.

## Contribution

It explicitly shows the cohomological equivalence of two superparticle formulations in 11D and analyzes their relation to supergravity.

## Key findings

- Cohomologies of the two models are equivalent under specific group decompositions.
- Pure spinor cohomology reproduces supergravity equations of motion.
- Light-cone analysis confirms the validity of the pure spinor approach.

## 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: $SO(10,1) \rightarrow SO(1,1)\times SO(9)$ and $SO(10,1) \rightarrow SO(3,1)\times SO(7)$. 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.