Canonical Covariant Formulation of Green-Schwarz Superstring without Second Class Constraints

TL;DR

This paper presents a new covariant Hamiltonian formulation of the Green-Schwarz superstring that simplifies the constraint structure, enabling consistent BRST quantization and reproducing light-cone gauge results.

Contribution

It introduces a covariant action with only first class constraints, generalizing previous superparticle actions and facilitating superstring quantization.

Findings

Constructed a covariant superstring action with only first class constraints

Derived the correct BRST operator for quantization

Reproduced light-cone gauge fixed action

Abstract

We describe a canonical covariant formulation of the Green-Schwarz Superstring which allows the construction of a new covariant action canonically equivalent to the Green-Schwarz action but subjected only to first class constraints. From this action the correct BRST operator for the quantization of the Green-Schwarz Superstring may be constructed. Also the gauge fixed action in the Light-Cone gauge may be reobtained. The action presented in this letter generalizes in a non-trivial form the action introduced by Kallosh for the Brink-Schwarz-Casalbuoni Superparticle.