On the Quantization of the GS String on $AdS_5 \times S^5$

TL;DR

This paper develops a method for quantizing the Green-Schwarz string on $AdS_5 imes S^5$, ensuring gauge consistency and matching supergravity predictions in the large radius limit.

Contribution

It introduces globally well-defined gauge fixing procedures and a perturbative quantization approach for the GS string in $AdS_5 imes S^5$, connecting string theory with supergravity results.

Findings

Consistent gauge fixing for kappa symmetry and diffeomorphisms.

Perturbative quantization in inverse radius expansion.

Agreement of vertex operators and correlators with supergravity.

Abstract

We discuss the quantization of the Green-Schwarz string action on $AdS_5 \times S^5$. We construct consistent, globally well-defined, gauge fixing choices for kappa symmetry and worldsheet diffeomorphism invariance. We then proceed to quantize the theory in a perturbation series in the inverse radius of curvature, in a background field expansion. We discuss vertex operators and correlation functions, and demonstrate agreement with supergravity results in the appropriate limit.