Boundary fluctuations of AdS string

We analyse the world-sheet perturbations of string theory formulated around AdS3 background. We identify a set of operators that, while added to the world-sheet action, generate the boundary fluctuations of AdS3. The effect of these operators can be collectively defined in terms of Liouville field living on the AdS3 boundary. We then study various deformations of AdS3 generated by boundary fluctuations by turning on suitable world-sheet couplings. We also discuss certain small fluctuations around the BTZ black hole.