The Green--Schwarz Superstring in Extended Configuration Space and Infinitely Reducible First Class Constraints Problem

TL;DR

This paper modifies the Green--Schwarz superstring action by adding trivial variables, resulting in a covariant and linearly independent set of constraints that address the reducibility problem in the theory.

Contribution

It introduces an extended configuration space for the superstring, unifying constraints and resolving reducibility issues with a covariant formulation.

Findings

Constraints are unified into a covariant set.

Reducibility is confined to second class constraints.

The extended formulation maintains $SO(1,9)$ covariance.

Abstract

The Green--Schwarz superstring action is modified to include some set of additional (on-shell trivial) variables. A complete constraints system of the theory turns out to be reducible both in the original and in additional variable sectors. The initial $8s$ first class constraints and $8c$ second class ones are shown to be unified with $8c$ first and $8s$ second class constraints from the additional variables sector, resulting with $SO(1,9)$-covariant and linearly independent constraint sets. Residual reducibility proves to fall on second class constraints only.