Operator Formulation of Green-Schwarz Superstring in the Semi-Light-Cone Conformal Gauge

TL;DR

This paper develops an operator-based framework for the Green-Schwarz superstring in the semi-light-cone gauge, preserving conformal invariance and enabling the construction of symmetry generators and vertex operators.

Contribution

It introduces a comprehensive operator formulation in the SLC gauge, including quantum symmetry algebras, BRST-invariant vertex operators, and a transformation linking to the light-cone gauge.

Findings

Constructed quantum Virasoro and super-Poincare generators.

Built BRST-invariant vertex operators for massless quanta.

Derived BRST-invariant DDF operators from light-cone oscillators.

Abstract

In this article we present a comprehensive account of the operator formulation of the Green-Schwarz superstring in the semi-light-cone (SLC) gauge, where the worldsheet conformal invariance is preserved. Starting from the basic action, we systematically study the symmetry structure of the theory in the SLC gauge both in the Lagrangian and the phase space formulations. After quantizing the theory in the latter formulation we construct the quantum Virasoro and the super-Poincare generators and clarify the closure properties of these symmetry algebras. Then by making full use of this knowledge we will be able to construct the BRST-invariant vertex operators which describe the emission and the absorption of the massless quanta and show that they form the appropriate representation of the quantum symmetry algebras. Furthermore, we will construct an exact quantum similarity transformation which connects the SLC gauge and the familiar light-cone (LC) gauge. As an application BRST-invariant DDF operators in the SLC gauge are obtained starting from the corresponding physical oscillators in the LC gauge.