Probing AdS/CFT correspondence via world-sheet methods and 2d gravity like scaling arguments

We show how some features of the AdS/CFT correspondence for AdS_3 can easily be understood via standard world-sheet methods and 2d gravity like scaling arguments. To do this, we propose a stringy way for perturbing two-dimensional CFT's around their critical points. Our strategy is to start from a stringy (world-sheet) representation of 2d CFT in space-time. Next we perturb a world-sheet action by some marginal operators such that the space-time symmetry becomes finite dimensional. As a result, we get a massive FT in space-time with a scale provided by two-dimensional coupling constant. It turns out that there exists a perturbation that leads to string theory on AdS_3. In this case the scale is equivalently provided by the radial anti-de-Sitter coordinate.