On the quantization of the GS string on AdS5×S5

We discuss the quantization of the Green-Schwarz string action on AdS5×S5. 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.