Towards relating the kappa-symmetric and pure-spinor versions of the supermembrane

TL;DR

This paper explores the connection between the kappa-symmetric and pure-spinor formulations of the supermembrane, proposing a method to relate their BRST charges through a topological sector and similarity transformation.

Contribution

It extends Berkovits' approach from superstrings to supermembranes, establishing a link between two formulations via a novel BRST charge construction.

Findings

Reinstatement of reparameterisation constraints in pure-spinor supermembrane

Introduction of a topological sector and similarity transformation to relate BRST charges

Identification of a supermembrane analogue of the superstring b ghost

Abstract

We study the relation between the kappa-symmetric formulation of the supermembrane in eleven dimensions and the pure-spinor version. Recently, Berkovits related the Green-Schwarz and pure-spinor superstrings. In this paper, we attempt to extend this method to the supermembrane. We show that it is possible to reinstate the reparameterisation constraints in the pure-spinor formulation of the supermembrane by introducing a topological sector and performing a similarity transformation. The resulting BRST charge is then of conventional type and is argued to be (related to) the BRST charge of the kappa-symmetric supermembrane in a formulation where all second class constraints are 'gauge unfixed' to first class constraints. In our analysis we also encounter a natural candidate for a (non-covariant) supermembrane analogue of the superstring b ghost.