Towards Pure Spinor Type Covariant Description of Supermembrane -- An Approach from the Double Spinor Formalism --

TL;DR

This paper extends a double spinor formalism from superstring theory to the supermembrane in 11 dimensions, constructing a covariant classical framework with a closed algebra of constraints, paving the way for future quantization.

Contribution

It introduces a classical double spinor formalism for the supermembrane, establishing a first order reducible algebra of constraints analogous to the superstring case.

Findings

Constructed a covariant classical supermembrane formalism

Established a closed algebra of first class constraints

Identified challenges for quantization

Abstract

In a previous work, we have constructed a reparametrization invariant worldsheet action from which one can derive the super-Poincare covariant pure spinor formalism for the superstring at the fully quantum level. The main idea was the doubling of the spinor degrees of freedom in the Green-Schwarz formulation together with the introduction of a new compensating local fermionic symmetry. In this paper, we extend this "double spinor" formalism to the case of the supermembrane in 11 dimensions at the classical level. The basic scheme works in parallel with the string case and we are able to construct the closed algebra of first class constraints which governs the entire dynamics of the system. A notable difference from the string case is that this algebra is first order reducible and the associated BRST operator must be constructed accordingly. The remaining problems which need to be solved for the quantization will also be discussed.